Title: Update and Enhance Our Research Group Summary for the Website ==================================================================================== Our goal is to create a concise, engaging, and factually accurate summary that captures our research group’s identity, achievements, and future ambitions—with a special focus on our artificial intelligence initiatives. ==================================================================================== Output Format (Markdown): ------------------------------------------------------------------------------------ --- layout: home --- ![AI generated image](/assets/images/index.png) Content generated by [gemini-1.5-pro](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/posts/index.md). Image generated by [imagen-3.0-generate-002](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/images/index.md). ------------------------------------------------------------------------------------ ==================================================================================== Section 1: Content Creation Instructions ==================================================================================== 1. **Compose the Website Summary:** - Write a clear, engaging narrative that is accessible to both experts and the general public. - The summary should include the following elements: - **Introduction:** Briefly describe who we are, our research areas, and our mission. - **Research Focus:** Highlight our primary research themes, innovative methodologies, and technical contributions, with special emphasis on AI. - **Highlight Achievements:** Mention key publications and significant milestones that underscore the impact of our work. - **Outline Future Directions:** Summarize emerging projects and research avenues. - When referring to any research topic, include a Markdown-formatted link to a relevant arXiv paper (e.g., [non-parametric reconstructions](https://arxiv.org/abs/2503.08658)). - Use bullet points, subheadings, or other formatting to enhance readability. - The name of the group is 'The Handley Research Group.' 2. **Integrate Data from Multiple Sources:** - **Published Papers (Markdown):** A list of all our published papers. These papers are available on arXiv, and you should include a link to each paper mentioned in the narrative. - **Research Group Structure (YAML):** The members of our group and our organizational history. There will not be a link to this, but you can use it to inform the narrative. - **Future Research Directions (LaTeX):** A successful grant application detailing our future research plans. There will not be a link to this, but you can use it to inform the narrative. Do not mention the grant application. - Seamlessly weave insights from these three sources into a cohesive and compelling narrative. 3. **Emphasize AI Research:** - Give particular attention to our work in artificial intelligence. When discussing AI-related topics, ensure to reference illustrative arXiv papers using proper Markdown link formatting. 4. **Final Formatting Requirements:** - The output must be plain Markdown; do not wrap it in Markdown code fences. - Preserve the YAML front matter exactly as provided. ==================================================================================== Section 2: Provided Data for Integration ==================================================================================== 1. **List of Published Papers:** ```markdown # On the accuracy of posterior recovery with neural network emulators [2503.13263](entry.id) ## Abstract Neural network emulators are widely used in astrophysics and cosmology to approximate complex simulations inside Bayesian inference loops. Ad hoc rules of thumb are often used to justify the emulator accuracy required for reliable posterior recovery. We provide a theoretically motivated limit on the maximum amount of incorrect information inferred by using an emulator with a given accuracy. Under assumptions of linearity in the model, uncorrelated noise in the data and a Gaussian likelihood function, we demonstrate that the difference between the true underlying posterior and the recovered posterior can be quantified via a Kullback-Leibler divergence. We demonstrate how this limit can be used in the field of 21-cm cosmology by comparing the posteriors recovered when fitting mock data sets generated with the 1D radiative transfer code ARES directly with the simulation code and separately with an emulator. This paper is partly in response to and builds upon recent discussions in the literature which call into question the use of emulators in Bayesian inference pipelines. Upon repeating some aspects of these analyses, we find these concerns quantitatively unjustified, with accurate posterior recovery possible even when the mean RMSE error for the emulator is approximately 20% of the magnitude of the noise in the data. For the purposes of community reproducibility, we make our analysis code public at this link https://github.com/htjb/validating_posteriors. ## Authors H. T. J. Bevins, T. Gessey-Jones, W. J. Handley ## Published 2025-03-17T15:17:15Z # Nonparametric reconstructions of dynamical dark energy via flexknots [2503.08658](entry.id) ## Abstract Recent cosmological surveys have provided unprecedented datasets that can be used to reconstruct the history of the dark energy equation of state. In this work, a free-form "flexknot'' parameterisation is employed to represent $w(a)$ as a linear spline between free-moving nodes, the number of which may vary. By combining DESI Baryon Acoustic Oscillation measurements with Pantheon+ or DES5Y supernovae, the functional posteriors of $w(a)$ reveal an unexpected W-shaped structure. While the Bayesian evidence may still favour $\Lambda$CDM, the robustness of these results suggests the structure is indeed present in the data. The tension $R$-statistic and suspiciousness have been marginalised over models, and demonstrate that while the reconstructions from DESI and Pantheon+ agree, DESI and DES5Y do not. We conclude that, while there is no smoking gun for dynamical dark energy, the structure unearthed in this work is generally too complex to be captured by the restrictive $w$CDM or CPL parameterisations. ## Authors A. N. Ormondroyd, W. J. Handley, M. P. Hobson, A. N. Lasenby ## Published 2025-03-11T17:47:49Z # Accounting for Noise and Singularities in Bayesian Calibration Methods for Global 21-cm Cosmology Experiments [2412.14023](entry.id) ## Abstract Due to the large dynamic ranges involved with separating the cosmological 21-cm signal from the Cosmic Dawn from galactic foregrounds, a well-calibrated instrument is essential to avoid biases from instrumental systematics. In this paper we present three methods for calibrating a global 21-cm cosmology experiment using the noise wave parameter formalisation to characterise a low noise amplifier including a careful consideration of how calibrator temperature noise and singularities will bias the result. The first method presented in this paper builds upon the existing conjugate priors method by weighting the calibrators by a physically motivated factor, thereby avoiding singularities and normalising the noise. The second method fits polynomials to the noise wave parameters by marginalising over the polynomial coefficients and sampling the polynomial orders as parameters. The third method introduces a physically motivated noise model to the marginalised polynomial method. Running these methods on a suite of simulated datasets based on the REACH receiver design and a lab dataset, we found that our methods produced a calibration solution which is equally as or more accurate than the existing conjugate priors method when compared with an analytic estimate of the calibrator's noise. We find in the case of the measured lab dataset the conjugate priors method is biased heavily by the large noise on the shorted load calibrator, resulting in incorrect noise wave parameter fits. This is mitigated by the methods introduced in this paper which calibrate the validation source spectra to within 5% of the noise floor. ## Authors Christian J. Kirkham, William J. Handley, Jiacong Zhu, Kaan Artuc, Ian L. V. Roque, Samuel A. K. Leeney, Harry T. J. Bevins, Dominic J. Anstey, Eloy de Lera Acedo ## Published 2024-12-18T16:40:37Z # Receiver design for the REACH global 21-cm signal experiment [2307.00099](entry.id) ## Abstract We detail the the REACH radiometric system designed to enable measurements of the 21-cm neutral hydrogen line. Included is the radiometer architecture and end-to-end system simulations as well as a discussion of the challenges intrinsic to highly-calibratable system development. Following this, we share laboratory results based on the calculation of noise wave parameters utilising an over-constrained least squares approach demonstrating a calibration RMSE of 80 mK for five hours of integration on a custom-made source with comparable impedance to that of the antenna used in the field. This paper therefore documents the state of the calibrator and data analysis in December 2022 in Cambridge before shipping to South Africa. ## Authors Ian L. V. Roque, Nima Razavi-Ghods, Steven H. Carey, John A. Ely, Will Handley, Alessio Magro, Riccardo Chiello, Tian Huang, P. Alexander, D. Anstey, G. Bernardi, H. T. J. Bevins, J. Cavillot, W. Croukamp, J. Cumner, E. de Lera Acedo, D. I. L. de Villiers, A. Fialkov, T. Gessey-Jones, Q. Gueuning, A. T. Josaitis, G. Kulkarni, S. A. K. Leeney, R. Maiolino, P. D. Meerburg, S. Mittal, M. Pagano, S. Pegwal, C. Pieterse, J. R. Pritchard, A. Saxena, K. H. Scheutwinkel, P. Scott, E. Shen, P. H. Sims, O. Smirnov, M. Spinelli, K. Zarb-Adami ## Published 2023-06-30T19:31:47Z # Cosmological Parameter Estimation with Sequential Linear Simulation-based Inference [2501.03921](entry.id) ## Abstract We develop the framework of Linear Simulation-based Inference (LSBI), an application of simulation-based inference where the likelihood is approximated by a Gaussian linear function of its parameters. We obtain analytical expressions for the posterior distributions of hyper-parameters of the linear likelihood in terms of samples drawn from a simulator, for both uniform and conjugate priors. This method is applied sequentially to several toy-models and tested on emulated datasets for the Cosmic Microwave Background temperature power spectrum. We find that convergence is achieved after four or five rounds of $\mathcal{O}(10^4)$ simulations, which is competitive with state-of-the-art neural density estimation methods. Therefore, we demonstrate that it is possible to obtain significant information gain and generate posteriors that agree with the underlying parameters while maintaining explainability and intellectual oversight. ## Authors Nicolas Mediato-Diaz, Will Handley ## Published 2025-01-07T16:34:47Z # The Bayesian Global Sky Model (B-GSM): Validation of a Data Driven Bayesian Simultaneous Component Separation and Calibration Algorithm for EoR Foreground Modelling [2501.01417](entry.id) ## Abstract We introduce the Bayesian Global Sky Model (B-GSM), a novel data-driven Bayesian approach to modelling radio foregrounds at frequencies <400~MHz. B-GSM aims to address the limitations of previous models by incorporating robust error quantification and calibration. Using nested sampling, we compute Bayesian evidence and posterior distributions for the spectral behaviour and spatial amplitudes of diffuse emission components. Bayesian model comparison is used to determine the optimal number of emission components and their spectral parametrisation. Posterior sky predictions are conditioned on both diffuse emission and absolute temperature datasets, enabling simultaneous component separation and calibration. B-GSM is validated against a synthetic dataset designed to mimic the partial sky coverage, thermal noise, and calibration uncertainties present in real observations of the diffuse sky at low frequencies. B-GSM correctly identifies a model parametrisation with two emission components featuring curved power-law spectra. The posterior sky predictions agree with the true synthetic sky within statistical uncertainty. We find that the root-mean-square (RMS) residuals between the true and posterior predictions for the sky temperature as a function of LST are significantly reduced, when compared to the uncalibrated dataset. This indicates that B-GSM is able to correctly calibrate its posterior sky prediction to the independent absolute temperature dataset. We find that while the spectral parameters and component amplitudes exhibit some sensitivity to prior assumptions, the posterior sky predictions remain robust across a selection of different priors. This is the first of two papers, and is focused on validation of B-GSMs Bayesian framework, the second paper will present results of deployment on real data and introduce the low-frequency sky model which will be available for public download. ## Authors George Carter, Will Handley, Mark Ashdown, Nima Razavi-Ghods ## Published 2025-01-02T18:58:03Z # Accelerated nested sampling with $β$-flows for gravitational waves [2411.17663](entry.id) ## Abstract There is an ever-growing need in the gravitational wave community for fast and reliable inference methods, accompanied by an informative error bar. Nested sampling satisfies the last two requirements, but its computational cost can become prohibitive when using the most accurate waveform models. In this paper, we demonstrate the acceleration of nested sampling using a technique called posterior repartitioning. This method leverages nested sampling's unique ability to separate prior and likelihood contributions at the algorithmic level. Specifically, we define a `repartitioned prior' informed by the posterior from a low-resolution run. To construct this repartitioned prior, we use a $\beta$-flow, a novel type of conditional normalizing flow designed to better learn deep tail probabilities. $\beta$-flows are trained on the entire nested sampling run and conditioned on an inverse temperature $\beta$. Applying our methods to simulated and real binary black hole mergers, we demonstrate how they can reduce the number of likelihood evaluations required for convergence by up to an order of magnitude, enabling faster model comparison and parameter estimation. Furthermore, we highlight the robustness of using $\beta$-flows over standard normalizing flows to accelerate nested sampling. Notably, $\beta$-flows successfully recover the same posteriors and evidences as traditional nested sampling, even in cases where standard normalizing flows fail. ## Authors Metha Prathaban, Harry Bevins, Will Handley ## Published 2024-11-26T18:26:20Z # On the spatial distribution of the Large-Scale structure: An Unsupervised search for Parity Violation [2410.16030](entry.id) ## Abstract We use machine learning methods to search for parity violations in the Large-Scale Structure (LSS) of the Universe, motivated by recent claims of chirality detection using the 4-Point Correlation Function (4PCF), which would suggest new physics during the epoch of inflation. This work seeks to reproduce these claims using methods originating from high energy collider analyses. Our machine learning methods optimise some underlying parity odd function of the data, and use it to evaluate the parity odd fraction. We demonstrate the effectiveness and suitability of these methods and then apply them to the Baryon Oscillation Spectroscopic Survey (BOSS) catalogue. No parity violation is detected at any significance. ## Authors Samuel Hewson, Will J. Handley, Christopher G. Lester ## Published 2024-10-21T14:05:16Z # Towards a Field Based Bayesian Evidence Inference from Nested Sampling Data [2408.09889](entry.id) ## Abstract Nested sampling (NS) is a stochastic method for computing the log-evidence of a Bayesian problem. It relies on stochastic estimates of prior volumes enclosed by likelihood contours, which limits the accuracy of the log-evidence calculation. We propose to transform the prior volume estimation into a Bayesian inference problem, which allows us to incorporate a smoothness assumption for likelihood-prior volume relations. As a result, we aim to increase the accuracy of the volume estimates and thus improve the overall log-evidence calculation using NS. The method presented works as a post-processing step for NS and provides posterior samples of the likelihood-prior-volume relation, from which the log-evidence can be calculated. We demonstrate an implementation of the algorithm and compare its results with plain NS on two synthetic datasets for which the underlying evidence is known. We find a significant improvement in accuracy for runs with less than one hundred active samples in NS, but are prone to numerical problems beyond this point. ## Authors Margret Westerkamp, Jakob Roth, Philipp Frank, Will Handley, Torsten Enßlin ## Published 2024-08-19T11:05:35Z # Predicting spatial curvature $Ω_K$ in globally $CPT$-symmetric universes [2407.18225](entry.id) ## Abstract Boyle and Turok's $CPT$-symmetric universe model posits that the universe was symmetric at the Big Bang, addressing numerous problems in both cosmology and the Standard Model of particle physics. We extend this model by incorporating the symmetric conditions at the end of the Universe, which impose constraints on the allowed perturbation modes. These constrained modes conflict with the integer wave vectors required by the global spatial geometry in a closed universe. To resolve this conflict, only specific values of curvature are permissible, and in particular the curvature density is constrained to be $\Omega_K \in \{-0.014, -0.009, -0.003, \ldots\}$, consistent with Planck observations. ## Authors Wei-Ning Deng, Will Handley ## Published 2024-07-25T17:46:24Z # Calibrating Bayesian Tension Statistics using Neural Ratio Estimation [2407.15478](entry.id) ## Abstract When fits of the same physical model to two different datasets disagree, we call this tension. Several apparent tensions in cosmology have occupied researchers in recent years, and a number of different metrics have been proposed to quantify tension. Many of these metrics suffer from limiting assumptions, and correctly calibrating these is essential if we want to successfully determine whether discrepancies are significant. A commonly used metric of tension is the evidence ratio R. The statistic has been widely adopted by the community as a Bayesian way of quantifying tensions, however, it has a non-trivial dependence on the prior that is not always accounted for properly. We show that this can be calibrated out effectively with Neural Ratio Estimation. We demonstrate our proposed calibration technique with an analytic example, a toy example inspired by 21-cm cosmology, and with observations of the Baryon Acoustic Oscillations from the Dark Energy Spectroscopic Instrument~(DESI) and the Sloan Digital Sky Survey~(SDSS). We find no significant tension between DESI and SDSS. ## Authors Harry T. J. Bevins, William J. Handley, Thomas Gessey-Jones ## Published 2024-07-22T08:46:11Z # Quantum initial conditions for curved inflating universes [2211.17248](entry.id) ## Abstract We discuss the challenges of motivating, constructing, and quantizing a canonically normalized inflationary perturbation in spatially curved universes. We show that this has historically proved challenging due to the interaction of nonadiabaticity with spatial curvature. We construct a novel curvature perturbation that is canonically normalized in the sense of its equation of motion and is unique up to a single scalar parameter. With this construction it becomes possible to set initial conditions invariant under canonical transformations, overcoming known ambiguities in the literature. This corrected quantization has potentially observational consequences via modifications to the primordial power spectrum at large angular scales, as well as theoretical implications for quantization procedures in curved cosmologies filled with a scalar field. ## Authors Mary I. Letey, Zakhar Shumaylov, Fruzsina J. Agocs, Will J. Handley, Michael P. Hobson, Anthony N. Lasenby ## Published 2022-11-30T18:48:07Z # Resonant or asymmetric: The status of sub-GeV dark matter [2405.17548](entry.id) ## Abstract Sub-GeV dark matter (DM) particles produced via thermal freeze-out evade many of the strong constraints on heavier DM candidates but at the same time face a multitude of new constraints from laboratory experiments, astrophysical observations and cosmological data. In this work we combine all of these constraints in order to perform frequentist and Bayesian global analyses of fermionic and scalar sub-GeV DM coupled to a dark photon with kinetic mixing. For fermionic DM, we find viable parameter regions close to the dark photon resonance, which expand significantly when including a particle-antiparticle asymmetry. For scalar DM, the velocity-dependent annihilation cross section evades the strongest constraints even in the symmetric case. Using Bayesian model comparison, we show that both asymmetric fermionic DM and symmetric scalar DM are preferred over symmetric fermionic DM due to the reduced fine-tuning penalty. Finally, we explore the discovery prospects of near-future experiments both in the full parameter space and for specific benchmark points. We find that the most commonly used benchmark scenarios are already in tension with existing constraints and propose a new benchmark point that can be targeted with future searches. ## Authors Sowmiya Balan, Csaba Balázs, Torsten Bringmann, Christopher Cappiello, Riccardo Catena, Timon Emken, Tomás E. Gonzalo, Taylor R. Gray, Will Handley, Quan Huynh, Felix Kahlhoefer, Aaron C. Vincent ## Published 2024-05-27T18:00:01Z # Fully Bayesian Forecasts with Evidence Networks [2309.06942](entry.id) ## Abstract Sensitivity forecasts inform the design of experiments and the direction of theoretical efforts. To arrive at representative results, Bayesian forecasts should marginalize their conclusions over uncertain parameters and noise realizations rather than picking fiducial values. However, this is typically computationally infeasible with current methods for forecasts of an experiment's ability to distinguish between competing models. We thus propose a novel simulation-based methodology capable of providing expedient and rigorous Bayesian model comparison forecasts without relying on restrictive assumptions. ## Authors T. Gessey-Jones, W. J. Handley ## Published 2023-09-13T13:25:04Z # Analytic Approximations for the Primordial Power Spectrum with Israel Junction Conditions [2309.15984](entry.id) ## Abstract This work compares cosmological matching conditions used in approximating generic pre-inflationary phases of the universe. We show that the joining conditions for primordial scalar perturbations assumed by Contaldi et al. are inconsistent with the physically motivated Israel junction conditions, however; performing general relativistic matching with the aforementioned constraints results in unrealistic primordial power spectra. Eliminating the need for ambiguous matching, we look at an alternative semi-analytic model for producing the primordial power spectrum allowing for finite duration cosmological phase transitions. ## Authors D. D. Dineen, W. J. Handley ## Published 2023-09-27T20:05:37Z # Costless correction of chain based nested sampling parameter estimation in gravitational wave data and beyond [2404.16428](entry.id) ## Abstract Nested sampling parameter estimation differs from evidence estimation, in that it incurs an additional source of error. This error affects estimates of parameter means and credible intervals in gravitational wave analyses and beyond, and yet, it is typically not accounted for in standard error estimation methods. In this paper, we present two novel methods to quantify this error more accurately for any chain based nested sampler, using the additional likelihood calls made at runtime in producing independent samples. Using injected signals of black hole binary coalescences as an example, we first show concretely that the usual error estimation method is insufficient to capture the true error bar on parameter estimates. We then demonstrate how the extra points in the chains of chain based samplers may be carefully utilised to estimate this error correctly, and provide a way to check the accuracy of the resulting error bars. Finally, we discuss how this error affects $p$-$p$ plots and coverage assessments. ## Authors Metha Prathaban, Will Handley ## Published 2024-04-25T08:58:57Z # A foundation model for atomistic materials chemistry [2401.00096](entry.id) ## Abstract Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model - and its qualitative and at times quantitative accuracy - on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, chemical reactions, interfaces and even the dynamics of a small protein. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry. ## Authors Ilyes Batatia, Philipp Benner, Yuan Chiang, Alin M. Elena, Dávid P. Kovács, Janosh Riebesell, Xavier R. Advincula, Mark Asta, Matthew Avaylon, William J. Baldwin, Fabian Berger, Noam Bernstein, Arghya Bhowmik, Samuel M. Blau, Vlad Cărare, James P. Darby, Sandip De, Flaviano Della Pia, Volker L. Deringer, Rokas Elijošius, Zakariya El-Machachi, Fabio Falcioni, Edvin Fako, Andrea C. Ferrari, Annalena Genreith-Schriever, Janine George, Rhys E. A. Goodall, Clare P. Grey, Petr Grigorev, Shuang Han, Will Handley, Hendrik H. Heenen, Kersti Hermansson, Christian Holm, Jad Jaafar, Stephan Hofmann, Konstantin S. Jakob, Hyunwook Jung, Venkat Kapil, Aaron D. Kaplan, Nima Karimitari, James R. Kermode, Namu Kroupa, Jolla Kullgren, Matthew C. Kuner, Domantas Kuryla, Guoda Liepuoniute, Johannes T. Margraf, Ioan-Bogdan Magdău, Angelos Michaelides, J. Harry Moore, Aakash A. Naik, Samuel P. Niblett, Sam Walton Norwood, Niamh O'Neill, Christoph Ortner, Kristin A. Persson, Karsten Reuter, Andrew S. Rosen, Lars L. Schaaf, Christoph Schran, Benjamin X. Shi, Eric Sivonxay, Tamás K. Stenczel, Viktor Svahn, Christopher Sutton, Thomas D. Swinburne, Jules Tilly, Cas van der Oord, Eszter Varga-Umbrich, Tejs Vegge, Martin Vondrák, Yangshuai Wang, William C. Witt, Fabian Zills, Gábor Csányi ## Published 2023-12-29T23:08:59Z # Bayesian approach to radio frequency interference mitigation [2211.15448](entry.id) ## Abstract Interfering signals such as Radio Frequency Interference from ubiquitous satellite constellations are becoming an endemic problem in fields involving physical observations of the electromagnetic spectrum. To address this we propose a novel data cleaning methodology. Contamination is simultaneously flagged and managed at the likelihood level. It is modeled in a Bayesian fashion through a piecewise likelihood that is constrained by a Bernoulli prior distribution. The techniques described in this paper can be implemented with just a few lines of code. ## Authors S. A. K. Leeney, W. J. Handley, E. de Lera Acedo ## Published 2022-11-28T15:43:25Z # On the Constraints on Superconducting Cosmic Strings from 21-cm Cosmology [2312.08828](entry.id) ## Abstract Constraints on the potential properties of superconducting cosmic strings provide an indirect probe of physics beyond the standard model at energies inaccessible to terrestrial particle colliders. In this study, we perform the first joint Bayesian analysis to extract constraints on superconducting cosmic strings from current 21-cm signal measurements while accounting rigorously for the uncertainties in foregrounds and high redshift astrophysics. We include the latest publicly available 21-cm power spectrum upper limits from HERA, 21-cm global signal data from SARAS 3, and the synergistic probe of the unresolved X-ray background in our final analysis. This paper thus constitutes the first attempt to use 21-cm power spectrum data to probe cosmic strings. In contrast to previous works, we find no strong constraints can be placed on superconducting cosmic strings from current 21-cm measurements. This is because of uncertainties in the X-ray emission efficiency of the first galaxies, with X-ray emissivities greater than $3 \times 10^{40}$erg s$^{-1}$ M$_{\odot}^{-1}$ yr able to mask the presence of cosmic strings in the 21-cm signal. We conclude by discussing the prospects for future constraints from definitive 21-cm signal measurements and argue that the recently proposed soft photon heating should be cause for optimism due to its potential to break degeneracies that would have otherwise made the signatures of cosmic strings difficult to distinguish from those of astrophysical origin. ## Authors T. Gessey-Jones, S. Pochinda, H. T. J. Bevins, A. Fialkov, W. J. Handley, E. de Lera Acedo, S. Singh, R. Barkana ## Published 2023-12-14T11:20:33Z # Kernel-, mean- and noise-marginalised Gaussian processes for exoplanet transits and $H_0$ inference [2311.04153](entry.id) ## Abstract Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. Kernel recovery and mean function inference were explored on synthetic data from exoplanet transit light curve simulations. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, $H_0$, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and $\Lambda$CDM-dependent baryon acoustic oscillation observations. The inferred $H_0$ values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are $H_0= 66 \pm 6\, \mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$, $H_0= 67 \pm 10\, \mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ and $H_0= 69 \pm 6\, \mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with $\ln R=12.17\pm 0.02$. ## Authors Namu Kroupa, David Yallup, Will Handley, Michael Hobson ## Published 2023-11-07T17:31:01Z # Piecewise Normalizing Flows [2305.02930](entry.id) ## Abstract Normalizing flows are an established approach for modelling complex probability densities through invertible transformations from a base distribution. However, the accuracy with which the target distribution can be captured by the normalizing flow is strongly influenced by the topology of the base distribution. A mismatch between the topology of the target and the base can result in a poor performance, as is typically the case for multi-modal problems. A number of different works have attempted to modify the topology of the base distribution to better match the target, either through the use of Gaussian Mixture Models (Izmailov et al., 2020; Ardizzone et al., 2020; Hagemann & Neumayer, 2021) or learned accept/reject sampling (Stimper et al., 2022). We introduce piecewise normalizing flows which divide the target distribution into clusters, with topologies that better match the standard normal base distribution, and train a series of flows to model complex multi-modal targets. We demonstrate the performance of the piecewise flows using some standard benchmarks and compare the accuracy of the flows to the approach taken in Stimper et al. (2022) for modelling multi-modal distributions. We find that our approach consistently outperforms the approach in Stimper et al. (2022) with a higher emulation accuracy on the standard benchmarks. ## Authors Harry Bevins, Will Handley, Thomas Gessey-Jones ## Published 2023-05-04T15:30:10Z # Inferring Evidence from Nested Sampling Data via Information Field Theory [2312.11907](entry.id) ## Abstract Nested sampling provides an estimate of the evidence of a Bayesian inference problem via probing the likelihood as a function of the enclosed prior volume. However, the lack of precise values of the enclosed prior mass of the samples introduces probing noise, which can hamper high-accuracy determinations of the evidence values as estimated from the likelihood-prior-volume function. We introduce an approach based on information field theory, a framework for non-parametric function reconstruction from data, that infers the likelihood-prior-volume function by exploiting its smoothness and thereby aims to improve the evidence calculation. Our method provides posterior samples of the likelihood-prior-volume function that translate into a quantification of the remaining sampling noise for the evidence estimate, or for any other quantity derived from the likelihood-prior-volume function. ## Authors Margret Westerkamp, Jakob Roth, Philipp Frank, Will Handley, Torsten Enßlin ## Published 2023-12-19T07:25:47Z # Joint analysis constraints on the physics of the first galaxies with low frequency radio astronomy data [2301.03298](entry.id) ## Abstract The first billion years of cosmic history remains largely unobserved. We demonstrate, using a novel machine learning technique, how combining upper limits on the spatial fluctuations in the 21-cm signal with observations of the sky-averaged 21-cm signal from neutral hydrogen can improve our understanding of this epoch. By jointly analysing data from SARAS3 (redshift $z\approx15-25$) and limits from HERA ($z\approx8$ and $10$), we show that such a synergetic analysis provides tighter constraints on the astrophysics of galaxies 200 million years after the Big Bang than can be achieved with the individual data sets. Although our constraints are weak, this is the first time data from a sky-averaged 21-cm experiment and power spectrum experiment have been analysed together. In synergy, the two experiments leave only $64.9^{+0.3}_{-0.1}$% of the explored broad theoretical parameter space to be consistent with the joint data set, in comparison to $92.3^{+0.3}_{-0.1}$% for SARAS3 and $79.0^{+0.5}_{-0.2}$% for HERA alone. We use the joint analysis to constrain star formation efficiency, minimum halo mass for star formation, X-ray luminosity of early emitters and the radio luminosity of early galaxies. The joint analysis disfavours at 68% confidence a combination of galaxies with X-ray emission that is $\lesssim 33$ and radio emission that is $\gtrsim 32$ times as efficient as present day galaxies. We disfavour at $95$% confidence scenarios in which power spectra are $\geq126$ mK$^{2}$ at $z=25$ and the sky-averaged signals are $\leq-277$ mK. ## Authors Harry T. J. Bevins, Stefan Heimersheim, Irene Abril-Cabezas, Anastasia Fialkov, Eloy de Lera Acedo, William Handley, Saurabh Singh, Rennan Barkana ## Published 2023-01-09T12:32:49Z # Marginal Post Processing of Bayesian Inference Products with Normalizing Flows and Kernel Density Estimators [2205.12841](entry.id) ## Abstract Bayesian analysis has become an indispensable tool across many different cosmological fields including the study of gravitational waves, the Cosmic Microwave Background and the 21-cm signal from the Cosmic Dawn among other phenomena. The method provides a way to fit complex models to data describing key cosmological and astrophysical signals and a whole host of contaminating signals and instrumental effects modelled with `nuisance parameters'. In this paper, we summarise a method that uses Masked Autoregressive Flows and Kernel Density Estimators to learn marginal posterior densities corresponding to core science parameters. We find that the marginal or 'nuisance-free' posteriors and the associated likelihoods have an abundance of applications including; the calculation of previously intractable marginal Kullback-Leibler divergences and marginal Bayesian Model Dimensionalities, likelihood emulation and prior emulation. We demonstrate each application using toy examples, examples from the field of 21-cm cosmology and samples from the Dark Energy Survey. We discuss how marginal summary statistics like the Kullback-Leibler divergences and Bayesian Model Dimensionalities can be used to examine the constraining power of different experiments and how we can perform efficient joint analysis by taking advantage of marginal prior and likelihood emulators. We package our multipurpose code up in the pip-installable code margarine for use in the wider scientific community. ## Authors Harry T. J. Bevins, William J. Handley, Pablo Lemos, Peter H. Sims, Eloy de Lera Acedo, Anastasia Fialkov, Justin Alsing ## Published 2022-05-25T15:10:15Z # Improving Gradient-guided Nested Sampling for Posterior Inference [2312.03911](entry.id) ## Abstract We present a performant, general-purpose gradient-guided nested sampling algorithm, ${\tt GGNS}$, combining the state of the art in differentiable programming, Hamiltonian slice sampling, clustering, mode separation, dynamic nested sampling, and parallelization. This unique combination allows ${\tt GGNS}$ to scale well with dimensionality and perform competitively on a variety of synthetic and real-world problems. We also show the potential of combining nested sampling with generative flow networks to obtain large amounts of high-quality samples from the posterior distribution. This combination leads to faster mode discovery and more accurate estimates of the partition function. ## Authors Pablo Lemos, Nikolay Malkin, Will Handley, Yoshua Bengio, Yashar Hezaveh, Laurence Perreault-Levasseur ## Published 2023-12-06T21:09:18Z # Non-Gaussian Likelihoods for Type Ia Supernovae Cosmology: Implications for Dark Energy and $H_0$ [2312.02075](entry.id) ## Abstract The latest improvements in the scale and calibration of Type Ia supernovae catalogues allow us to constrain the specific nature and evolution of dark energy through its effect on the expansion history of the universe. We present the results of Bayesian cosmological model comparison on the SNe~Ia catalogue Pantheon+, where Flat $\Lambda$CDM is preferred by the data over all other models and we find moderate evidence ($\Delta \log \mathcal{Z} \sim 2.5$) to reject a number of the alternate dark energy models. The effect of peculiar velocity corrections on model comparison is analysed, where we show that removing the peculiar velocity corrections results in a varying fit on non-$\Lambda$CDM parameters. As well as comparing cosmological models, the Bayesian methodology is extended to comparing the scatter model of the data, testing for non-gaussianity in the Pantheon+ Hubble residuals. We find that adding a scale parameter to the Pantheon+ covariances, or alternately using a multivariate Student's t-distribution fits the data better than the fiducial analysis, producing a cosmology independent evidence increase of $\Delta \log \mathcal{Z} = 2.29 $ and $2.46$ respectively. This improved treatment of the scatter decreases the uncertainty in the constraint on the Hubble constant, finding $H_0 = 73.67 \pm 0.99 $ km s$^{-1}$ Mpc$^{-1}$, in $ 5.7 \sigma$ tension with Planck. We also explore $M_B$ transition models as a potential solution for the Hubble tension, finding no evidence to support these models among the SNe data. ## Authors Toby Lovick, Suhail Dhawan, Will Handley ## Published 2023-12-04T17:39:47Z # Balancing ACT: weighing prior dependency and global tensions of DR6 lensing with other datasets [2310.08490](entry.id) ## Abstract We provide a complementary nested sampling analysis for the Atacama Cosmology Telescope lensing data release 6. This allows the quantification of global consistency statistics between ACT lensing and alternative datasets. In the context of flat $\Lambda$CDM, we find no inconsistency between ACT, Baryonic Acoustic Oscillations, Planck anisotropies, weak lensing datasets, or NPIPE lensing. As part of our analysis, we also investigate the effect of the prior widths used in the ACT analysis and find that the headline results are quantitatively but not qualitatively affected by the chosen priors. We use both Bayes factors and the suspiciousness statistic to quantify the possibility of tension, and find suspiciousness unsuitable in the case of strong agreement between ACT DR6 and NPIPE. Nested sampling provides a competitive alternative to Metropolis Hastings and we recommend it be used alongside existing analyses. We release the chains and plotting source for the analysis using anesthetic. ## Authors A. N. Ormondroyd, W. J. Handley, M. P. Hobson, A. N. Lasenby ## Published 2023-10-12T16:49:11Z # aeons: approximating the end of nested sampling [2312.00294](entry.id) ## Abstract This paper presents analytic results on the anatomy of nested sampling, from which a technique is developed to estimate the run-time of the algorithm that works for any nested sampling implementation. We test these methods on both toy models and true cosmological nested sampling runs. The method gives an order-of-magnitude prediction of the end point at all times, forecasting the true endpoint within standard error around the halfway point. ## Authors Zixiao Hu, Artem Baryshnikov, Will Handley ## Published 2023-12-01T02:18:58Z # A General Bayesian Framework to Account for Foreground Map Errors in Global 21-cm Experiments [2211.10448](entry.id) ## Abstract Measurement of the global 21-cm signal during Cosmic Dawn (CD) and the Epoch of Reionization (EoR) is made difficult by bright foreground emission which is 2-5 orders of magnitude larger than the expected signal. Fitting for a physics-motivated parametric forward model of the data within a Bayesian framework provides a robust means to separate the signal from the foregrounds, given sufficient information about the instrument and sky. It has previously been demonstrated that, within such a modelling framework, a foreground model of sufficient fidelity can be generated by dividing the sky into $N$ regions and scaling a base map assuming a distinct uniform spectral index in each region. Using the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) as our fiducial instrument, we show that, if unaccounted-for, amplitude errors in low-frequency radio maps used for our base map model will prevent recovery of the 21-cm signal within this framework, and that the level of bias in the recovered 21-cm signal is proportional to the amplitude and the correlation length of the base-map errors in the region. We introduce an updated foreground model that is capable of accounting for these measurement errors by fitting for a monopole offset and a set of spatially-dependent scale factors describing the ratio of the true and model sky temperatures, with the size of the set determined by Bayesian evidence-based model comparison. We show that our model is flexible enough to account for multiple foreground error scenarios allowing the 21-cm sky-averaged signal to be detected without bias from simulated observations with a smooth conical log spiral antenna. ## Authors Michael Pagano, Peter Sims, Adrian Liu, Dominic Anstey, Will Handley, Eloy De Lera Acedo ## Published 2022-11-18T19:00:00Z # Signatures of Cosmic Ray Heating in 21-cm Observables [2304.07201](entry.id) ## Abstract Cosmic rays generated by supernovae carry away a significant portion of the lifetime energy emission of their parent star, making them a plausible mechanism for heating the early universe intergalactic medium (IGM). Following a review of the existing literature on cosmic ray heating, we develop a flexible model of this heating mechanism for use in 3D semi-numerical 21-cm signal simulations and conduct the first investigations of the signatures it imprints on the 21-cm power spectrum and tomographic maps. We find that cosmic ray heating of the IGM is short-ranged, leading to heating clustered around star-forming sites, and a sharp contrast between heated regions of 21-cm emission and unheated regions of absorption. This contrast results in greater small-scale power for cosmic ray heated scenarios compared to what is found for X-ray heating, thus suggesting a way to test the nature of IGM heating with future 21-cm observations. Finally, we find an unexpectedly rich thermal history in models where cosmic rays can only escape efficiently from low-mass halos, such as in scenarios where these energetic particles originate from population III star supernovae remnants. The interplay of heating and the Lyman-Werner feedback in these models can produce a local peak in the IGM kinetic temperature and, for a limited parameter range, a flattened absorption trough in the global 21-cm signal. ## Authors T. Gessey-Jones, A. Fialkov, E. de Lera Acedo, W. J. Handley, R. Barkana ## Published 2023-04-14T15:27:35Z # Hunting for bumps in the margins [2211.10391](entry.id) ## Abstract Data driven modelling is vital to many analyses at collider experiments, however the derived inference of physical properties becomes subject to details of the model fitting procedure. This work brings a principled Bayesian picture, based on the marginal likelihood, of both data modelling and signal extraction to a common collider physics scenario. First the marginal likelihood based method is used to propose a more principled construction of the background process, systematically exploring a variety of candidate shapes. Second the picture is extended to propose the marginal likelihood as a useful tool for anomaly detection challenges in particle physics. This proposal offers insight into both precise background model determination and demonstrates a flexible method to extend signal determination beyond a simple bump hunt. ## Authors David Yallup, Will Handley ## Published 2022-11-18T17:48:13Z # Sky-averaged 21-cm signal extraction using multiple antennas with an SVD framework: the REACH case [2212.07415](entry.id) ## Abstract In a sky-averaged 21-cm signal experiment, the uncertainty on the extracted signal depends mainly on the covariance between the foreground and 21-cm signal models. In this paper, we construct these models using the modes of variation obtained from the Singular Value Decomposition of a set of simulated foreground and 21-cm signals. We present a strategy to reduce this overlap between the 21-cm and foreground modes by simultaneously fitting the spectra from multiple different antennas, which can be used in combination with the method of utilizing the time dependence of foregrounds while fitting multiple drift scan spectra. To demonstrate this idea, we consider two different foreground models (i) a simple foreground model, where we assume a constant spectral index over the sky, and (ii) a more realistic foreground model, with a spatial variation of the spectral index. For the simple foreground model, with just a single antenna design, we are able to extract the signal with good accuracy if we simultaneously fit the data from multiple time slices. The 21-cm signal extraction is further improved when we simultaneously fit the data from different antennas as well. This improvement becomes more pronounced while using the more realistic mock observations generated from the detailed foreground model. We find that even if we fit multiple time slices, the recovered signal is biased and inaccurate for a single antenna. However, simultaneously fitting the data from different antennas reduces the bias and the uncertainty by a factor of 2-3 on the extracted 21-cm signal. ## Authors Anchal Saxena, P. Daniel Meerburg, Eloy de Lera Acedo, Will Handley, Léon V. E. Koopmans ## Published 2022-12-14T18:55:15Z # Bayesian evidence-driven likelihood selection for sky-averaged 21-cm signal extraction [2204.04491](entry.id) ## Abstract We demonstrate that the Bayesian evidence can be used to find a good approximation of the ground truth likelihood function of a dataset, a goal of the likelihood-free inference (LFI) paradigm. As a concrete example, we use forward modelled sky-averaged 21-cm signal antenna temperature datasets where we artificially inject noise structures of various physically motivated forms. We find that the Gaussian likelihood performs poorly when the noise distribution deviates from the Gaussian case e.g. heteroscedastic radiometric or heavy-tailed noise. For these non-Gaussian noise structures, we show that the generalised normal likelihood is on a similar Bayesian evidence scale with comparable sky-averaged 21-cm signal recovery as the ground truth likelihood function of our injected noise. We therefore propose the generalised normal likelihood function as a good approximation of the true likelihood function if the noise structure is a priori unknown. ## Authors K. H. Scheutwinkel, W. Handley, E. de Lera Acedo ## Published 2022-04-09T14:57:47Z # Use of Time Dependent Data in Bayesian Global 21cm Foreground and Signal Modelling [2210.04707](entry.id) ## Abstract Global 21cm cosmology aims to investigate the cosmic dawn and epoch of reionisation by measuring the sky averaged HI absorption signal, which requires, accurate modelling of, or correction for, the bright radio foregrounds and distortions arising from chromaticity of the antenna beam. We investigate the effect of improving foreground modelling by fitting data sets from many observation times simultaneously in a single Bayesian analysis, fitting for the same parameter set by performing these fits on simulated data. We find that for a hexagonal dipole antenna, this simultaneous fitting produces a significant improvement in the accuracy of the recovered 21cm signal, relative to fitting a time average of the data. Furthermore, the recovered models of the foreground are also seen to become more accurate by up to a factor of $\sim$2-3 relative to time averaged fitting. For a less chromatic log spiral antenna, no significant improvement in signal recovery was found by this process. However, the modelling of the foregrounds was still significantly improved. We also investigate extending this technique to fit multiple data sets from different antennae simultaneously for the same parameters. This is also found to improve both 21cm signal and foreground modelling, to a higher degree than fitting data set from multiple times from the same antenna. ## Authors Dominic Anstey, Eloy de Lera Acedo, Will Handley ## Published 2022-10-10T14:07:00Z # Radio antenna design for sky-averaged 21 cm cosmology experiments: the REACH case [2109.10098](entry.id) ## Abstract Following the reported detection of an absorption profile associated with the 21~cm sky-averaged signal from the Cosmic Dawn by the EDGES experiment in 2018, a number of experiments have been set up to verify this result. This paper discusses the design process used for global 21~cm experiments, focusing specifically on the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH). This experiment will seek to understand and compensate for systematic errors present using detailed modelling and characterization of the instrumentation. There is detailed the quantitative figures of merit and numerical modelling used to assist the design process of the REACH dipole antenna (one of the 2 antenna designs for REACH Phase I). This design process produced a 2.5:1 frequency bandwidth dipole. The aim of this design was to balance spectral smoothness and low impedance reflections with the ability to describe and understand the antenna response to the sky signal to inform the critically important calibration during observation and data analysis. ## Authors J. Cumner, E. De Lera Acedo, D. I. L. de Villiers, D. Anstey, C. I. Kolitsidas, B. Gurdon, N. Fagnoni, P. Alexander, G. Bernardi, H. T. J. Bevins, S. Carey, J. Cavillot, R. Chiello, C. Craeye, W. Croukamp, J. A. Ely, A. Fialkov, T. Gessey-Jones, Q. Gueuning, W. Handley, R. Hills, A. T. Josaitis, G. Kulkarni, A. Magro, R. Maiolino, P. D. Meerburg, S. Mittal, J. R. Pritchard, E. Puchwein, N. Razavi-Ghods, I. L. V. Roque, A. Saxena, K. H. Scheutwinkel, E. Shen, P. H. Sims, O. Smirnov, M. Spinelli, K. Zarb-Adami ## Published 2021-09-21T11:06:44Z # Cosmological constraints on decaying axion-like particles: a global analysis [2205.13549](entry.id) ## Abstract Axion-like particles (ALPs) decaying into photons are known to affect a wide range of astrophysical and cosmological observables. In this study we focus on ALPs with masses in the keV-MeV range and lifetimes between $10^4$ and $10^{13}$ seconds, corresponding to decays between the end of Big Bang Nucleosynthesis and the formation of the Cosmic Microwave Background (CMB). Using the CosmoBit module of the global fitting framework GAMBIT, we combine state-of-the-art calculations of the irreducible ALP freeze-in abundance, primordial element abundances (including photodisintegration through ALP decays), CMB spectral distortions and anisotropies, and constraints from supernovae and stellar cooling. This approach makes it possible for the first time to perform a global analysis of the ALP parameter space while varying the parameters of $\Lambda$CDM as well as several nuisance parameters. We find a lower bound on the ALP mass of around $m_a > 300\,\text{keV}$, which can only be evaded if ALPs are stable on cosmological timescales. Future observations of CMB spectral distortions with a PIXIE-like mission are expected to improve this bound by two orders of magnitude. ## Authors Csaba Balázs, Sanjay Bloor, Tomás E. Gonzalo, Will Handley, Sebastian Hoof, Felix Kahlhoefer, Marie Lecroq, David J. E. Marsh, Janina J. Renk, Pat Scott, Patrick Stöcker ## Published 2022-05-26T18:00:00Z # SuperNest: accelerated nested sampling applied to astrophysics and cosmology [2212.01760](entry.id) ## Abstract We present a method for improving the performance of nested sampling as well as its accuracy. Building on previous work by Chen et al., we show that posterior repartitioning may be used to reduce the amount of time nested sampling spends in compressing from prior to posterior if a suitable ``proposal'' distribution is supplied. We showcase this on a cosmological example with a Gaussian posterior, and release the code as an LGPL licensed, extensible Python package https://gitlab.com/a-p-petrosyan/sspr. ## Authors Aleksandr Petrosyan, William James Handley ## Published 2022-12-04T08:04:01Z # Astrophysical Constraints from the SARAS3 non-detection of the Cosmic Dawn Sky-Averaged 21-cm Signal [2212.00464](entry.id) ## Abstract Observations of the redshifted 21-cm line of atomic hydrogen have resulted in several upper limits on the 21-cm power spectrum and a tentative detection of the sky-averaged signal at $z\sim17$. Made with the EDGES Low-Band antenna, this claim was recently disputed by the SARAS3 experiment, which reported a non-detection and is the only available upper limit strong enough to constrain cosmic dawn astrophysics. We use these data to constrain a population of radio-luminous galaxies $\sim 200$ million years after the Big Bang ($z\approx 20$). We find, using Bayesian data analysis, that the data disfavours (at 68% confidence) radio-luminous galaxies in dark matter halos with masses of $4.4\times10^{5}$ M$_\odot \lesssim M \lesssim 1.1\times10^{7}$M$_\odot$ (where $M_\odot$ is the mass of the Sun) at $z = 20$ and galaxies in which $>5$% of the gas is converted into stars. The data disfavour galaxies with radio luminosity per star formation rate of $L_\mathrm{r}/\mathrm{SFR} \gtrsim 1.549 \times 10^{25}$ W Hz$^{-1}$M$_\odot^{-1}$ yr at 150 MHz, a thousand times brighter than today, and, separately, a synchrotron radio background in excess of the CMB by $\gtrsim 6%$ at 1.42 GHz. ## Authors H. T. J. Bevins, A. Fialkov, E. de Lera Acedo, W. J. Handley, S. Singh, R. Subrahmanyan, R. Barkana ## Published 2022-12-01T12:34:31Z # Marginal Bayesian Statistics Using Masked Autoregressive Flows and Kernel Density Estimators with Examples in Cosmology [2207.11457](entry.id) ## Abstract Cosmological experiments often employ Bayesian workflows to derive constraints on cosmological and astrophysical parameters from their data. It has been shown that these constraints can be combined across different probes such as Planck and the Dark Energy Survey and that this can be a valuable exercise to improve our understanding of the universe and quantify tension between multiple experiments. However, these experiments are typically plagued by differing systematics, instrumental effects and contaminating signals, which we collectively refer to as `nuisance' components, that have to be modelled alongside target signals of interest. This leads to high dimensional parameter spaces, especially when combining data sets, with > 20 dimensions of which only around 5 correspond to key physical quantities. We present a means by which to combine constraints from different data sets in a computationally efficient manner by generating rapid, reusable and reliable marginal probability density estimators, giving us access to nuisance-free likelihoods. This is possible through the unique combination of nested sampling, which gives us access to Bayesian evidences, and the marginal Bayesian statistics code MARGARINE. Our method is lossless in the signal parameters, resulting in the same posterior distributions as would be found from a full nested sampling run over all nuisance parameters, and typically quicker than evaluating full likelihoods. We demonstrate our approach by applying it to the combination of posteriors from the Dark Energy Survey and Planck. ## Authors Harry Bevins, Will Handley, Pablo Lemos, Peter Sims, Eloy de Lera Acedo, Anastasia Fialkov ## Published 2022-07-23T08:24:50Z # The REACH radiometer for detecting the 21-cm hydrogen signal from redshift 7.5 to 28 [2210.07409](entry.id) ## Abstract Observations of the 21-cm line from primordial hydrogen promise to be one of the best tools to study the early epochs of the Universe: the Dark Ages, the Cosmic Dawn, and the subsequent Epoch of Reionization. In 2018, the EDGES experiment caught the attention of the cosmology community with a potential detection of an absorption feature in the sky-averaged radio spectrum centred at 78 MHz. The feature is deeper than expected, and, if confirmed, would call for new physics. However, different groups have re-analyzed the EDGES data and questioned the reliability of the signal. The Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) is a sky-averaged 21-cm experiment aiming at improving the current observations by tackling the issues faced by current instruments related to residual systematic signals in the data. The novel experimental approach focuses on detecting and jointly explaining these systematics together with the foregrounds and the cosmological signal using Bayesian statistics. To achieve this, REACH features simultaneous observations with two different antennas, an ultra wideband system (redshift range 7.5 to 28), and a receiver calibrator based on in-field measurements. Simulated observations forecast percent-level constraints on astrophysical parameters, potentially opening up a new window to the infant Universe. ## Authors E. de Lera Acedo, D. I. L. de Villiers, N. Razavi-Ghods, W. Handley, A. Fialkov, A. Magro, D. Anstey, H. T. J. Bevins, R. Chiello, J. Cumner, A. T. Josaitis, I. L. V. Roque, P. H. Sims, K. H. Scheutwinkel, P. Alexander, G. Bernardi, S. Carey, J. Cavillot, W. Croukamp, J. A. Ely, T. Gessey-Jones, Q. Gueuning, R. Hills, G. Kulkarni, R. Maiolino, P. D. Meerburg, S. Mittal, J. R. Pritchard, E. Puchwein, A. Saxena, E. Shen, O. Smirnov, M. Spinelli, K. Zarb-Adami ## Published 2022-10-13T23:13:21Z # Bayesian evidence-driven diagnosis of instrumental systematics for sky-averaged 21-cm cosmology experiments [2204.04445](entry.id) ## Abstract We demonstrate the effectiveness of a Bayesian evidence-based analysis for diagnosing and disentangling the sky-averaged 21-cm signal from instrumental systematic effects. As a case study, we consider a simulated REACH pipeline with an injected systematic. We demonstrate that very poor performance or erroneous signal recovery is achieved if the systematic remains unmodelled. These effects include sky-averaged 21-cm posterior estimates resembling a very deep or wide signal. However, when including parameterised models of the systematic, the signal recovery is dramatically improved in performance. Most importantly, a Bayesian evidence-based model comparison is capable of determining whether or not such a systematic model is needed as the true underlying generative model of an experimental dataset is in principle unknown. We, therefore, advocate a pipeline capable of testing a variety of potential systematic errors with the Bayesian evidence acting as the mechanism for detecting their presence. ## Authors K. H. Scheutwinkel, E. de Lera Acedo, W. Handley ## Published 2022-04-09T10:34:06Z # Exploring phase space with Nested Sampling [2205.02030](entry.id) ## Abstract We present the first application of a Nested Sampling algorithm to explore the high-dimensional phase space of particle collision events. We describe the adaptation of the algorithm, designed to perform Bayesian inference computations, to the integration of partonic scattering cross sections and the generation of individual events distributed according to the corresponding squared matrix element. As a first concrete example we consider gluon scattering processes into 3-, 4- and 5-gluon final states and compare the performance with established sampling techniques. Starting from a flat prior distribution Nested Sampling outperforms the Vegas algorithm and achieves results comparable to a dedicated multi-channel importance sampler. We outline possible approaches to combine Nested Sampling with non-flat prior distributions to further reduce the variance of integral estimates and to increase unweighting efficiencies. ## Authors David Yallup, Timo Janßen, Steffen Schumann, Will Handley ## Published 2022-05-04T12:41:00Z # Impact of the Primordial Stellar Initial Mass Function on the 21-cm Signal [2202.02099](entry.id) ## Abstract Properties of the first generation of stars (Pop III), such as their initial mass function (IMF), are poorly constrained by observations and have yet to converge between simulations. The cosmological 21-cm signal of neutral hydrogen is predicted to be sensitive to Lyman-band photons produced by these stars, thus providing a unique way to probe the first stellar population. In this paper, we investigate the impacts of the Pop III IMF on the cosmic dawn 21-cm signal via the Wouthuysen-Field effect, Lyman-Werner feedback, Ly-alpha heating, and CMB heating. We calculate the emission spectra of star-forming halos for different IMFs by integrating over individual metal-free stellar spectra, computed from a set of stellar evolution histories and stellar atmospheres, and taking into account variability of the spectra with stellar age. Through this study, we therefore relax two common assumptions: that the zero-age main sequence emission rate of a Pop III star is representative of its lifetime mean emission rate, and that Pop III emission can be treated as instantaneous. Exploring a bottom-heavy, a top-heavy, and intermediate IMFs, we show that variations in the 21-cm signal are driven by stars lighter than 20 solar masses. For the explored models we find maximum relative differences of 59% in the cosmic dawn global 21-cm signal, and 131% between power spectra. Although this impact is modest, precise modelling of the first stars and their evolution is necessary for accurate prediction and interpretation of the 21-cm signal. ## Authors T. Gessey-Jones, N. S. Sartorio, A. Fialkov, G. M. Mirouh, M. Magg, R. G. Izzard, E. de Lera Acedo, W. J. Handley, R. Barkana ## Published 2022-02-04T12:17:01Z # Primordial power spectra from $k$-inflation with curvature [2112.07547](entry.id) ## Abstract We investigate the primordial power spectra for general kinetic inflation models that support a period of kinetic dominance in the case of curved universes. We present derivations of the Mukhanov-Sasaki equations with a nonstandard scalar kinetic Lagrangian which manifests itself through the inflationary sound speed $c_s^2$. We extend the analytical approximations exploited in Contaldi et al [1] and Thavanesan et al [2] to general kinetic Lagrangians and show the effect of $k$-inflation on the primordial power spectra for models with curvature. In particular, the interplay between sound speed and curvature results in a natural low wavenumber cutoff for the power spectra in the case of closed universes. Using the analytical approximation, we further show that a change in the inflationary sound speed between different epochs of inflation results in non-decaying oscillations in the resultant power spectra for the comoving curvature perturbation. ## Authors Zakhar Shumaylov, Will Handley ## Published 2021-12-14T16:56:06Z # Rescuing Palindromic Universes with Improved Recombination Modelling [2111.14588](entry.id) ## Abstract We explore the linearly quantised primordial power spectra associated with palindromic universes. Extending the results of Lasenby et al. [1] and Bartlett et al. [2], we improve the modelling of recombination and include higher orders in the photonic Boltzmann hierarchy. In so doing, we find that the predicted power spectra become largely consistent with observational data. The improved recombination modelling involves developing further techniques for dealing with the future conformal boundary, by integrating the associated perturbation equations both forwards and backwards in conformal time. The resulting wavevector quantisation gives a lowest allowed wavenumber ${k_0 = 9.93 \times 10^{-5} \textrm{Mpc}^{-1}}$ and linear spacing ${\Delta k = 1.63 \times 10^{-4} \textrm{Mpc}^{-1}}$, providing fits consistent with observational data equivalent in quality to the $\Lambda$CDM model. ## Authors Metha Prathaban, Will Handley ## Published 2021-11-29T15:20:32Z # Nested sampling for physical scientists [2205.15570](entry.id) ## Abstract We review Skilling's nested sampling (NS) algorithm for Bayesian inference and more broadly multi-dimensional integration. After recapitulating the principles of NS, we survey developments in implementing efficient NS algorithms in practice in high-dimensions, including methods for sampling from the so-called constrained prior. We outline the ways in which NS may be applied and describe the application of NS in three scientific fields in which the algorithm has proved to be useful: cosmology, gravitational-wave astronomy, and materials science. We close by making recommendations for best practice when using NS and by summarizing potential limitations and optimizations of NS. ## Authors Greg Ashton, Noam Bernstein, Johannes Buchner, Xi Chen, Gábor Csányi, Andrew Fowlie, Farhan Feroz, Matthew Griffiths, Will Handley, Michael Habeck, Edward Higson, Michael Hobson, Anthony Lasenby, David Parkinson, Livia B. Pártay, Matthew Pitkin, Doris Schneider, Joshua S. Speagle, Leah South, John Veitch, Philipp Wacker, David J. Wales, David Yallup ## Published 2022-05-31T07:21:52Z # Analytical approximations for curved primordial power spectra [2009.05573](entry.id) ## Abstract We extend the work of Contaldi et al. and derive analytical approximations for primordial power spectra arising from models of inflation which include primordial spatial curvature. These analytical templates are independent of any specific inflationary potential and therefore illustrate and provide insight into the generic effects and predictions of primordial curvature, manifesting as cut-offs and oscillations at low multipoles and agreeing with numerical calculations. We identify through our analytical approximation that the effects of curvature can be mathematically attributed to shifts in the wavevectors participating dynamically. ## Authors Ayngaran Thavanesan, Denis Werth, Will Handley ## Published 2020-09-11T17:59:56Z # Split personalities in Bayesian Neural Networks: the case for full marginalisation [2205.11151](entry.id) ## Abstract The true posterior distribution of a Bayesian neural network is massively multimodal. Whilst most of these modes are functionally equivalent, we demonstrate that there remains a level of real multimodality that manifests in even the simplest neural network setups. It is only by fully marginalising over all posterior modes, using appropriate Bayesian sampling tools, that we can capture the split personalities of the network. The ability of a network trained in this manner to reason between multiple candidate solutions dramatically improves the generalisability of the model, a feature we contend is not consistently captured by alternative approaches to the training of Bayesian neural networks. We provide a concise minimal example of this, which can provide lessons and a future path forward for correctly utilising the explainability and interpretability of Bayesian neural networks. ## Authors David Yallup, Will Handley, Mike Hobson, Anthony Lasenby, Pablo Lemos ## Published 2022-05-23T09:24:37Z # A Comprehensive Bayesian re-analysis of the SARAS2 data from the Epoch of Reionization [2201.11531](entry.id) ## Abstract We present a Bayesian re-analysis of the sky-averaged 21-cm experimental data from SARAS2 using nested sampling implemented with polychord, spectrally smooth foreground modelling implemented with maxsmooth, detailed systematic modelling and rapid signal emulation with globalemu. Our analysis differs from previous analysis of the SARAS2 data through the use of a full Bayesian framework and separate modelling of the foreground and non-smooth systematics. We use the most up-to-date signal models including Lyman-$\alpha$ and CMB heating parameterised by astrophysical parameters such as star formation efficiency, X-ray heating efficiency, minimal virial circular velocity of star forming galaxies, CMB optical depth and the low energy cutoff of the X-ray spectral energy distribution. We consider models with an excess radio background above the CMB produced via radio emission from early galaxies and parameterised by a radio production efficiency. A non-smooth systematic is identified and modelled as both a frequency damped sinusoid introduced by the electronics and separately from the sky. The latter is modulated by the total efficiency of the antenna and marginally favoured by the data. We consider three different models for the noise in the data. The SARAS2 constraints on individual astrophysical parameters are extremely weak however we identify classes of disfavoured signals. We weakly disfavour standard astrophysical models with high Lyman-$\alpha$ fluxes and weak heating and more confidently disfavour exotic models with high Lyman-$\alpha$ fluxes, low X-ray efficiencies and high radio production efficiencies in early galaxies. ## Authors H. T. J. Bevins, E. de Lera Acedo, A. Fialkov, W. J. Handley, S. Singh, R. Subrahmanyan, R. Barkana ## Published 2022-01-27T14:11:14Z # Finite inflation in curved space [2205.07374](entry.id) ## Abstract We investigate the effects of non-zero spatial curvature on cosmic inflation in the light of cosmic microwave background (CMB) anisotropy measurements from the Planck 2018 legacy release and from the 2015 observing season of BICEP2 and the Keck Array. Even a small percentage of non-zero curvature today would significantly limit the total number of e-folds of the scale factor during inflation, rendering just-enough inflation scenarios with a kinetically dominated or fast-roll stage prior to slow-roll inflation more likely. Finite inflation leads to oscillations and a cutoff towards large scales in the primordial power spectrum and curvature pushes them into the CMB observable window. Using nested sampling, we carry out Bayesian parameter estimations and model comparisons taking into account constraints from reheating and horizon considerations. We confirm the preference of CMB data for closed universes with Bayesian odds of over $100:1$ and with a posterior on the curvature density parameter of $\Omega_{K,0}=-0.051\pm0.017$ for a curvature extension of LCDM and $\Omega_{K,0}=-0.031\pm0.014$ for Starobinsky inflation. Model comparisons of various inflation models give similar results as for flat universes with the Starobinsky model outperforming most other models. ## Authors Lukas T. Hergt, Fruzsina J. Agocs, Will J. Handley, Michael P. Hobson, Anthony N. Lasenby ## Published 2022-05-15T20:34:34Z # Improved cosmological fits with quantized primordial power spectra [2104.01938](entry.id) ## Abstract We observationally examine cosmological models based on primordial power spectra with quantized wavevectors. Introducing a linearly quantized power spectrum with $k_0=3.225\times10^{-4}\mathrm{Mpc}^{-1}$ and spacing $\Delta k = 2.257 \times 10^{-4} \mathrm{Mpc}^{-1}$ provides a better fit to the Planck 2018 observations than the concordance baseline, with $\Delta \chi^2 = -8.55$. Extending the results of Lasenby et al [1], we show that the requirement for perturbations to remain finite beyond the future conformal boundary in a universe containing dark matter and a cosmological constant results in a linearly quantized primordial power spectrum. It is found that the infrared cutoffs for this future conformal boundary quantized cosmology do not provide cosmic microwave background power spectra compatible with observations, but future theories may predict more observationally consistent quantized spectra. ## Authors D. J. Bartlett, W. J. Handley, A. N. Lasenby ## Published 2021-04-05T14:53:21Z # Perturbations and the Future Conformal Boundary [2104.02521](entry.id) ## Abstract The concordance model of cosmology predicts a universe which finishes in a finite amount of conformal time at a future conformal boundary. We show that for particular cases we study, the background variables and perturbations may be analytically continued beyond this boundary and that the "end of the universe" is not necessarily the end of their physical development. Remarkably, these theoretical considerations of the end of the universe might have observable consequences today: perturbation modes consistent with these boundary conditions have a quantised power spectrum which may be relevant to features seen in the large scale cosmic microwave background. Mathematically these cosmological models may either be interpreted as a palindromic universe mirrored in time, a reflecting boundary condition, or a double cover, but are identical with respect to their observational predictions and stand in contrast to the predictions of conformal cyclic cosmologies. ## Authors A. N. Lasenby, W. J. Handley, D. J. Bartlett, C. S. Negreanu ## Published 2021-04-05T14:53:07Z # Simple and statistically sound recommendations for analysing physical theories [2012.09874](entry.id) ## Abstract Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at https://doi.org/10.5281/zenodo.4322283. ## Authors Shehu S. AbdusSalam, Fruzsina J. Agocs, Benjamin C. Allanach, Peter Athron, Csaba Balázs, Emanuele Bagnaschi, Philip Bechtle, Oliver Buchmueller, Ankit Beniwal, Jihyun Bhom, Sanjay Bloor, Torsten Bringmann, Andy Buckley, Anja Butter, José Eliel Camargo-Molina, Marcin Chrzaszcz, Jan Conrad, Jonathan M. Cornell, Matthias Danninger, Jorge de Blas, Albert De Roeck, Klaus Desch, Matthew Dolan, Herbert Dreiner, Otto Eberhardt, John Ellis, Ben Farmer, Marco Fedele, Henning Flächer, Andrew Fowlie, Tomás E. Gonzalo, Philip Grace, Matthias Hamer, Will Handley, Julia Harz, Sven Heinemeyer, Sebastian Hoof, Selim Hotinli, Paul Jackson, Felix Kahlhoefer, Kamila Kowalska, Michael Krämer, Anders Kvellestad, Miriam Lucio Martinez, Farvah Mahmoudi, Diego Martinez Santos, Gregory D. Martinez, Satoshi Mishima, Keith Olive, Ayan Paul, Markus Tobias Prim, Werner Porod, Are Raklev, Janina J. Renk, Christopher Rogan, Leszek Roszkowski, Roberto Ruiz de Austri, Kazuki Sakurai, Andre Scaffidi, Pat Scott, Enrico Maria Sessolo, Tim Stefaniak, Patrick Stöcker, Wei Su, Sebastian Trojanowski, Roberto Trotta, Yue-Lin Sming Tsai, Jeriek Van den Abeele, Mauro Valli, Aaron C. Vincent, Georg Weiglein, Martin White, Peter Wienemann, Lei Wu, Yang Zhang ## Published 2020-12-17T19:00:06Z # Nested sampling for frequentist computation: fast estimation of small $p$-values [2105.13923](entry.id) ## Abstract We propose a novel method for computing $p$-values based on nested sampling (NS) applied to the sampling space rather than the parameter space of the problem, in contrast to its usage in Bayesian computation. The computational cost of NS scales as $\log^2{1/p}$, which compares favorably to the $1/p$ scaling for Monte Carlo (MC) simulations. For significances greater than about $4\sigma$ in both a toy problem and a simplified resonance search, we show that NS requires orders of magnitude fewer simulations than ordinary MC estimates. This is particularly relevant for high-energy physics, which adopts a $5\sigma$ gold standard for discovery. We conclude with remarks on new connections between Bayesian and frequentist computation and possibilities for tuning NS implementations for still better performance in this setting. ## Authors Andrew Fowlie, Sebastian Hoof, Will Handley ## Published 2021-05-27T15:06:03Z # Thermal WIMPs and the Scale of New Physics: Global Fits of Dirac Dark Matter Effective Field Theories [2106.02056](entry.id) ## Abstract We assess the status of a wide class of WIMP dark matter (DM) models in light of the latest experimental results using the global fitting framework $\textsf{GAMBIT}$. We perform a global analysis of effective field theory (EFT) operators describing the interactions between a gauge-singlet Dirac fermion and the Standard Model quarks, the gluons and the photon. In this bottom-up approach, we simultaneously vary the coefficients of 14 such operators up to dimension 7, along with the DM mass, the scale of new physics and several nuisance parameters. Our likelihood functions include the latest data from $\mathit{Planck}$, direct and indirect detection experiments, and the LHC. For DM masses below 100 GeV, we find that it is impossible to satisfy all constraints simultaneously while maintaining EFT validity at LHC energies. For new physics scales around 1 TeV, our results are influenced by several small excesses in the LHC data and depend on the prescription that we adopt to ensure EFT validity. Furthermore, we find large regions of viable parameter space where the EFT is valid and the relic density can be reproduced, implying that WIMPs can still account for the DM of the universe while being consistent with the latest data. ## Authors The GAMBIT Collaboration, Peter Athron, Neal Avis Kozar, Csaba Balázs, Ankit Beniwal, Sanjay Bloor, Torsten Bringmann, Joachim Brod, Christopher Chang, Jonathan M. Cornell, Ben Farmer, Andrew Fowlie, Tomás E. Gonzalo, Will Handley, Felix Kahlhoefer, Anders Kvellestad, Farvah Mahmoudi, Markus T. Prim, Are Raklev, Janina J. Renk, Andre Scaffidi, Pat Scott, Patrick Stöcker, Aaron C. Vincent, Martin White, Sebastian Wild, Jure Zupan ## Published 2021-06-03T18:00:17Z # A General Bayesian Framework for Foreground Modelling and Chromaticity Correction for Global 21cm Experiments [2010.09644](entry.id) ## Abstract The HI 21cm absorption line is masked by bright foregrounds and systematic distortions that arise due to the chromaticity of the antenna used to make the observation coupling to the spectral inhomogeneity of these foregrounds. We demonstrate that these distortions are sufficient to conceal the 21cm signal when the antenna is not perfectly achromatic and that simple corrections assuming a constant spatial distribution of foreground power are insufficient to overcome them. We then propose a new physics-motivated method of modelling the foregrounds of 21cm experiments in order to fit the chromatic distortions as part of the foregrounds. This is done by generating a simulated sky model across the observing band by dividing the sky into $N$ regions and scaling a base map assuming a distinct uniform spectral index in each region. The resulting sky map can then be convolved with a model of the antenna beam to give a model of foregrounds and chromaticity parameterised by the spectral indices of the $N$ regions. We demonstrate that fitting this model for varying $N$ using a Bayesian nested sampling algorithm and comparing the results using the evidence allows the 21cm signal to be reliably detected in data of a relatively smooth conical log spiral antenna. We also test a much more chromatic conical sinuous antenna and find this model will not produce a reliable signal detection, but in a manner that is easily distinguishable from a true detection. ## Authors Dominic Anstey, Eloy de Lera Acedo, Will Handley ## Published 2020-10-19T16:38:59Z # Informing antenna design for sky-averaged 21-cm experiments using a simulated Bayesian data analysis pipeline [2106.10193](entry.id) ## Abstract Global 21cm experiments aim to measure the sky averaged HI absorption signal from cosmic dawn and the epoch of reionisation. However, antenna chromaticity coupling to bright foregrounds can introduce distortions into the observational data of such experiments. We demonstrate a method for guiding the antenna design of a global experiment through data analysis simulations. This is done by performing simulated observations for a range of inserted 21cm signals, then attempting to identify the signals with a data analysis pipeline. We demonstrate this method on five antennae that were considered as potential designs for the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH); a conical log spiral antenna, an inverted conical sinuous antenna and polygonal-, square- and elliptical-bladed dipoles. We find that the log spiral performs significantly better than the other antennae tested, able to correctly and confidently identify every inserted 21cm signal. In second place is the polygonal dipole antenna, which was only unable to detect signals with both very low amplitudes of 0.05K and low centre frequency of 80MHz. The conical sinuous antenna was found to perform least accurately, only able to detect the highest amplitude 21cm signals, and even then with biases. We also demonstrate that, due to the non-trivial nature of chromatic distortion and the processes of correcting for it, these are not the results that could have been expected superficially from the extent of chromatic variation in each antenna. ## Authors Dominic Anstey, John Cumner, Eloy de Lera Acedo, Will Handley ## Published 2021-06-18T15:49:31Z # GLOBALEMU: A novel and robust approach for emulating the sky-averaged 21-cm signal from the cosmic dawn and epoch of reionisation [2104.04336](entry.id) ## Abstract Emulation of the Global (sky-averaged) 21-cm signal with neural networks has been shown to be an essential tool for physical signal modelling. In this paper we present globalemu, a Global 21-cm signal emulator that uses redshift as a character defining variable alongside a set of astrophysical parameters to estimate the signal brightness temperature. Combined with physically-motivated data pre-processing this makes for a reliable and fast emulator that is relatively insensitive to the network design. globalemu can emulate a high resolution signal in 1.3 ms in comparison to 133 ms, a factor of 102 improvement, when using the existing public state of the art 21cmGEM. We illustrate, with the standard astrophysical models used to train 21cmGEM, that globalemu is almost twice as accurate and for a test set of $\approx1,700$ signals we achieve a mean RMSE of 2.52 mK across the band z=7-28 ($\approx$10 per cent the expected noise of the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH)). The models are parameterised by the star formation efficiency, $f_*$, minimum virial circular velocity, $V_c$, X-ray efficiency, $f_X$, CMB optical depth, $\tau$, the slope and low energy cut off of the X-ray spectral energy density, $\alpha$ and $\nu_\mathrm{min}$, and the mean free path of ionizing photons, $R_\mathrm{mfp}$. globalemu provides a flexible framework for easily emulating updated simulations of the Global signal and in addition the neutral fraction history. The emulator is pip installable and available at: \url{https://github.com/htjb/globalemu}. globalemu will be used extensively by the REACH collaboration. ## Authors H. T. J. Bevins, W. J. Handley, A. Fialkov, E. de Lera Acedo, K. Javid ## Published 2021-04-09T12:48:52Z # Constraining Quantum Initial Conditions before Inflation [2104.03016](entry.id) ## Abstract We theoretically and observationally investigate different choices of initial conditions for the primordial mode function that are imposed during an epoch preceding inflation. By deriving predictions for the observables resulting from several alternate quantum vacuum prescriptions we show some choices of vacua are theoretically observationally distinguishable from others. Comparing these predictions to the Planck 2018 observations via a Bayesian analysis shows no significant evidence to favour any of the quantum vacuum prescriptions over the others. In addition we consider frozen initial conditions, representing a white-noise initial state at the big-bang singularity. Under certain assumptions the cosmological concordance model and frozen initial conditions are found to produce identical predictions for the cosmic microwave background anisotropies. Frozen initial conditions may thus provide an alternative theoretic paradigm to explain observations that were previously understood in terms of the inflation of a quantum vacuum. ## Authors T. Gessey-Jones, W. J. Handley ## Published 2021-04-07T09:42:46Z # Planck 2018 results. VI. Cosmological parameters [1807.06209](entry.id) ## Abstract We present cosmological parameter results from the final full-mission Planck measurements of the CMB anisotropies. We find good consistency with the standard spatially-flat 6-parameter $\Lambda$CDM cosmology having a power-law spectrum of adiabatic scalar perturbations (denoted "base $\Lambda$CDM" in this paper), from polarization, temperature, and lensing, separately and in combination. A combined analysis gives dark matter density $\Omega_c h^2 = 0.120\pm 0.001$, baryon density $\Omega_b h^2 = 0.0224\pm 0.0001$, scalar spectral index $n_s = 0.965\pm 0.004$, and optical depth $\tau = 0.054\pm 0.007$ (in this abstract we quote $68\,\%$ confidence regions on measured parameters and $95\,\%$ on upper limits). The angular acoustic scale is measured to $0.03\,\%$ precision, with $100\theta_*=1.0411\pm 0.0003$. These results are only weakly dependent on the cosmological model and remain stable, with somewhat increased errors, in many commonly considered extensions. Assuming the base-$\Lambda$CDM cosmology, the inferred late-Universe parameters are: Hubble constant $H_0 = (67.4\pm 0.5)$km/s/Mpc; matter density parameter $\Omega_m = 0.315\pm 0.007$; and matter fluctuation amplitude $\sigma_8 = 0.811\pm 0.006$. We find no compelling evidence for extensions to the base-$\Lambda$CDM model. Combining with BAO we constrain the effective extra relativistic degrees of freedom to be $N_{\rm eff} = 2.99\pm 0.17$, and the neutrino mass is tightly constrained to $\sum m_\nu< 0.12$eV. The CMB spectra continue to prefer higher lensing amplitudes than predicted in base -$\Lambda$CDM at over $2\,\sigma$, which pulls some parameters that affect the lensing amplitude away from the base-$\Lambda$CDM model; however, this is not supported by the lensing reconstruction or (in models that also change the background geometry) BAO data. (Abridged) ## Authors Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, R. Battye, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, J. Carron, A. Challinor, H. C. Chiang, J. Chluba, L. P. L. Colombo, C. Combet, D. Contreras, B. P. Crill, F. Cuttaia, P. de Bernardis, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, S. Dusini, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, M. Farhang, J. Fergusson, R. Fernandez-Cobos, F. Finelli, F. Forastieri, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Herranz, S. R. Hildebrandt, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, L. Knox, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, P. Lemos, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Lilley, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, M. Martinelli, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. Millea, S. Mitra, M. -A. Miville-Deschênes, D. Molinari, L. Montier, G. Morgante, A. Moss, P. Natoli, H. U. Nørgaard-Nielsen, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, H. V. Peiris, F. Perrotta, V. Pettorino, F. Piacentini, L. Polastri, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, E. P. S. Shellard, C. Sirignano, G. Sirri, L. D. Spencer, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, L. Valenziano, J. Valiviita, B. Van Tent, L. Vibert, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, M. White, S. D. M. White, A. Zacchei, A. Zonca ## Published 2018-07-17T04:05:07Z # Nested sampling with any prior you like [2102.12478](entry.id) ## Abstract Nested sampling is an important tool for conducting Bayesian analysis in Astronomy and other fields, both for sampling complicated posterior distributions for parameter inference, and for computing marginal likelihoods for model comparison. One technical obstacle to using nested sampling in practice is the requirement (for most common implementations) that prior distributions be provided in the form of transformations from the unit hyper-cube to the target prior density. For many applications - particularly when using the posterior from one experiment as the prior for another - such a transformation is not readily available. In this letter we show that parametric bijectors trained on samples from a desired prior density provide a general-purpose method for constructing transformations from the uniform base density to a target prior, enabling the practical use of nested sampling under arbitrary priors. We demonstrate the use of trained bijectors in conjunction with nested sampling on a number of examples from cosmology. ## Authors Justin Alsing, Will Handley ## Published 2021-02-24T18:45:13Z # Strengthening the bound on the mass of the lightest neutrino with terrestrial and cosmological experiments [2009.03287](entry.id) ## Abstract We determine the upper limit on the mass of the lightest neutrino from the most robust recent cosmological and terrestrial data. Marginalizing over possible effective relativistic degrees of freedom at early times ($N_\mathrm{eff}$) and assuming normal mass ordering, the mass of the lightest neutrino is less than 0.037 eV at 95% confidence; with inverted ordering, the bound is 0.042 eV. These results improve upon the strength and robustness of other recent limits and constrain the mass of the lightest neutrino to be barely larger than the largest mass splitting. We show the impacts of realistic mass models, and different sources of $N_\mathrm{eff}$. ## Authors The GAMBIT Cosmology Workgroup, :, Patrick Stöcker, Csaba Balázs, Sanjay Bloor, Torsten Bringmann, Tomás E. Gonzalo, Will Handley, Selim Hotinli, Cullan Howlett, Felix Kahlhoefer, Janina J. Renk, Pat Scott, Aaron C. Vincent, Martin White ## Published 2020-09-07T17:52:43Z # Bayesian noise wave calibration for 21-cm global experiments [2011.14052](entry.id) ## Abstract Detection of millikelvin-level signals from the 'Cosmic Dawn' requires an unprecedented level of sensitivity and systematic calibration. We report the theory behind a novel calibration algorithm developed from the formalism introduced by the EDGES collaboration for use in 21-cm experiments. Improvements over previous approaches are provided through the incorporation of a Bayesian framework and machine learning techniques such as the use of Bayesian evidence to determine the level of frequency variation of calibration parameters that is supported by the data, the consideration of correlation between calibration parameters when determining their values and the use of a conjugate-prior based approach that results in a fast algorithm for application in the field. In self-consistency tests using empirical data models of varying complexity, our methodology is used to calibrate a 50 $\Omega$ ambient-temperature load. The RMS error between the calibration solution and the measured temperature of the load is 8 mK, well within the 1$\sigma$ noise level. Whilst the methods described here are more applicable to global 21-cm experiments, they can easily be adapted and applied to other applications, including telescopes such as HERA and the SKA. ## Authors I. L. V. Roque, W. J. Handley, N. Razavi-Ghods ## Published 2020-11-28T03:10:40Z # When tension is just a fluctuation: How noisy data affect model comparison [2102.09547](entry.id) ## Abstract Summary statistics of the likelihood, such as the Bayesian evidence, offer a principled way of comparing models and assessing tension between, or within, the results of physical experiments. Noisy realisations of the data induce scatter in these model comparison statistics. For a realistic case of cosmological inference from large-scale structure we show that the logarithm of the Bayes factor attains scatter of order unity, increasing significantly with stronger tension between the models under comparison. We develop an approximate procedure that quantifies the sampling distribution of the evidence at small additional computational cost and apply it to real data to demonstrate the impact of the scatter, which acts to reduce the significance of any model discrepancies. Data compression is highlighted as a potential avenue to suppressing noise in the evidence to negligible levels, with a proof of concept on Planck cosmic microwave background data. ## Authors B. Joachimi, F. Köhlinger, W. Handley, P. Lemos ## Published 2021-02-18T18:49:48Z # Quantifying the global parameter tensions between ACT, SPT and Planck [2007.08496](entry.id) ## Abstract The overall cosmological parameter tension between the Atacama Cosmology Telescope 2020 (ACT) and Planck 2018 data within the concordance cosmological model is quantified using the suspiciousness statistic to be 2.6$\sigma$. Between ACT and the South Pole Telescope (SPT) we find a tension of 2.4$\sigma$, and 2.8$\sigma$ between ACT and Planck+SPT combined. While it is unclear whether the tension is caused by statistical fluctuations, systematic effects or new physics, caution should be exercised in combining these cosmic microwave background datasets in the context of the $\Lambda$CDM standard model of the universe. ## Authors Will Handley, Pablo Lemos ## Published 2020-07-16T17:48:00Z # Rapid numerical solutions for the Mukhanov-Sasaki equation [1809.11095](entry.id) ## Abstract We develop a novel technique for numerically computing the primordial power spectra of comoving curvature perturbations. By finding suitable analytic approximations for different regions of the mode equations and stitching them together, we reduce the solution of a differential equation to repeated matrix multiplication. This results in a wavenumber-dependent increase in speed which is orders of magnitude faster than traditional approaches at intermediate and large wavenumbers. We demonstrate the method's efficacy on the challenging case of a stepped quadratic potential with kinetic dominance initial conditions. ## Authors W. I. J. Haddadin, W. J. Handley ## Published 2018-09-28T15:38:24Z # A comparison of optimisation algorithms for high-dimensional particle and astrophysics applications [2101.04525](entry.id) ## Abstract Optimisation problems are ubiquitous in particle and astrophysics, and involve locating the optimum of a complicated function of many parameters that may be computationally expensive to evaluate. We describe a number of global optimisation algorithms that are not yet widely used in particle astrophysics, benchmark them against random sampling and existing techniques, and perform a detailed comparison of their performance on a range of test functions. These include four analytic test functions of varying dimensionality, and a realistic example derived from a recent global fit of weak-scale supersymmetry. Although the best algorithm to use depends on the function being investigated, we are able to present general conclusions about the relative merits of random sampling, Differential Evolution, Particle Swarm Optimisation, the Covariance Matrix Adaptation Evolution Strategy, Bayesian Optimisation, Grey Wolf Optimisation, and the PyGMO Artificial Bee Colony, Gaussian Particle Filter and Adaptive Memory Programming for Global Optimisation algorithms. ## Authors The DarkMachines High Dimensional Sampling Group, Csaba Balázs, Melissa van Beekveld, Sascha Caron, Barry M. Dillon, Ben Farmer, Andrew Fowlie, Eduardo C. Garrido-Merchán, Will Handley, Luc Hendriks, Guðlaugur Jóhannesson, Adam Leinweber, Judita Mamužić, Gregory D. Martinez, Sydney Otten, Pat Scott, Roberto Ruiz de Austri, Zachary Searle, Bob Stienen, Joaquin Vanschoren, Martin White ## Published 2021-01-12T14:48:58Z # maxsmooth: Rapid Maximally Smooth Function Fitting With Applications in Global 21-cm Cosmology [2007.14970](entry.id) ## Abstract Maximally Smooth Functions (MSFs) are a form of constrained functions in which there are no inflection points or zero crossings in high order derivatives. Consequently, they have applications to signal recovery in experiments where signals of interest are expected to be non-smooth features masked by larger smooth signals or foregrounds. They can also act as a powerful tool for diagnosing the presence of systematics. The constrained nature of MSFs makes fitting these functions a non-trivial task. We introduce maxsmooth, an open source package that uses quadratic programming to rapidly fit MSFs. We demonstrate the efficiency and reliability of maxsmooth by comparison to commonly used fitting routines and show that we can reduce the fitting time by approximately two orders of magnitude. We introduce and implement with maxsmooth Partially Smooth Functions, which are useful for describing elements of non-smooth structure in foregrounds. This work has been motivated by the problem of foreground modelling in 21-cm cosmology. We discuss applications of maxsmooth to 21-cm cosmology and highlight this with examples using data from the Experiment to Detect the Global Epoch of Reionization Signature (EDGES) and the Large-aperture Experiment to Detect the Dark Ages (LEDA) experiments. We demonstrate the presence of a sinusoidal systematic in the EDGES data with a log-evidence difference of $86.19\pm0.12$ when compared to a pure foreground fit. MSFs are applied to data from LEDA for the first time in this paper and we identify the presence of sinusoidal systematics. maxsmooth is pip installable and available for download at: https://github.com/htjb/maxsmooth ## Authors H. T. J. Bevins, W. J. Handley, A. Fialkov, E. de Lera Acedo, L. J. Greenhill, D. C. Price ## Published 2020-07-29T17:29:18Z # Nested sampling with plateaus [2010.13884](entry.id) ## Abstract It was recently emphasised by Riley (2019); Schittenhelm & Wacker (2020) that that in the presence of plateaus in the likelihood function nested sampling (NS) produces faulty estimates of the evidence and posterior densities. After informally explaining the cause of the problem, we present a modified version of NS that handles plateaus and can be applied retrospectively to NS runs from popular NS software using anesthetic. In the modified NS, live points in a plateau are evicted one by one without replacement, with ordinary NS compression of the prior volume after each eviction but taking into account the dynamic number of live points. The live points are replenished once all points in the plateau are removed. We demonstrate it on a number of examples. Since the modification is simple, we propose that it becomes the canonical version of Skilling's NS algorithm. ## Authors Andrew Fowlie, Will Handley, Liangliang Su ## Published 2020-10-26T20:21:04Z # Bayesian evidence for the tensor-to-scalar ratio $r$ and neutrino masses $m_ν$: Effects of uniform vs logarithmic priors [2102.11511](entry.id) ## Abstract We review the effect that the choice of a uniform or logarithmic prior has on the Bayesian evidence and hence on Bayesian model comparisons when data provide only a one-sided bound on a parameter. We investigate two particular examples: the tensor-to-scalar ratio $r$ of primordial perturbations and the mass of individual neutrinos $m_\nu$, using the cosmic microwave background temperature and polarisation data from Planck 2018 and the NuFIT 5.0 data from neutrino oscillation experiments. We argue that the Kullback-Leibler divergence, also called the relative entropy, mathematically quantifies the Occam penalty. We further show how the Bayesian evidence stays invariant upon changing the lower prior bound of an upper constrained parameter. While a uniform prior on the tensor-to-scalar ratio disfavours the $r$-extension compared to the base LCDM model with odds of about 1:20, switching to a logarithmic prior renders both models essentially equally likely. LCDM with a single massive neutrino is favoured over an extension with variable neutrino masses with odds of 20:1 in case of a uniform prior on the lightest neutrino mass, which decreases to roughly 2:1 for a logarithmic prior. For both prior options we get only a very slight preference for the normal over the inverted neutrino hierarchy with Bayesian odds of about 3:2 at most. ## Authors Lukas T. Hergt, Will J. Handley, Michael P. Hobson, Anthony N. Lasenby ## Published 2021-02-23T06:00:31Z # Convergent Bayesian Global Fits of 4D Composite Higgs Models [2101.00428](entry.id) ## Abstract Models in which the Higgs boson is a composite pseudo-Nambu-Goldstone boson offer attractive solutions to the Higgs mass naturalness problem. We consider three such models based on the minimal $SO(5) \rightarrow SO(4)$ symmetry breaking pattern, and perform convergent global fits on the models under a Bayesian framework in order to find the regions of their parameter spaces that best fit a wide range of constraints, including recent Higgs measurements. We use a novel technique to analyse the fine-tuning of the models, quantifying the tuning as the Kullback-Leibler divergence from the prior to the posterior probability on the parameter space. Each model is found to be able to satisfy all constraints at the $3\sigma$ level simultaneously. As a by-product of the fits, we analyse the collider phenomenology of our models in these viable regions. In two of the three models, we find that the $g g \rightarrow H \rightarrow \gamma \gamma$ cross section is less than ${\sim}90$% that predicted by the SM, which is already in slight tension with experiment and could potentially be ruled out in the future high-luminosity run of the LHC. In addition, the lightest fermions $F$ arising from the new strong dynamics in these models are seen in general to lie above ${\sim}1.1$ TeV, with the $F \rightarrow tW^{+}$ and $F \rightarrow \bar{b}W^{+}$ decays offering particularly promising channels for probing these models in future collider searches. ## Authors Ethan Carragher, Will Handley, Daniel Murnane, Peter Stangl, Wei Su, Martin White, Anthony G. Williams ## Published 2021-01-02T11:29:06Z # CosmoBit: A GAMBIT module for computing cosmological observables and likelihoods [2009.03286](entry.id) ## Abstract We introduce $\sf{CosmoBit}$, a module within the open-source $\sf{GAMBIT}$ software framework for exploring connections between cosmology and particle physics with joint global fits. $\sf{CosmoBit}$ provides a flexible framework for studying various scenarios beyond $\Lambda$CDM, such as models of inflation, modifications of the effective number of relativistic degrees of freedom, exotic energy injection from annihilating or decaying dark matter, and variations of the properties of elementary particles such as neutrino masses and the lifetime of the neutron. Many observables and likelihoods in $\sf{CosmoBit}$ are computed via interfaces to $\sf{AlterBBN}$, $\sf{CLASS}$, $\sf{DarkAges}$, $\sf{MontePython}$, $\sf{MultiModeCode}$, and $\sf{plc}$. This makes it possible to apply a wide range of constraints from large-scale structure, Type Ia supernovae, Big Bang Nucleosynthesis and the cosmic microwave background. Parameter scans can be performed using the many different statistical sampling algorithms available within the $\sf{GAMBIT}$ framework, and results can be combined with calculations from other $\sf{GAMBIT}$ modules focused on particle physics and dark matter. We include extensive validation plots and a first application to scenarios with non-standard relativistic degrees of freedom and neutrino temperature, showing that the corresponding constraint on the sum of neutrino masses is much weaker than in the standard scenario. ## Authors The GAMBIT Cosmology Workgroup, :, Janina J. Renk, Patrick Stöcker, Sanjay Bloor, Selim Hotinli, Csaba Balázs, Torsten Bringmann, Tomás E. Gonzalo, Will Handley, Sebastian Hoof, Cullan Howlett, Felix Kahlhoefer, Pat Scott, Aaron C. Vincent, Martin White ## Published 2020-09-07T17:52:43Z # The HARPS search for southern extra-solar planets XLV. Two Neptune mass planets orbiting HD 13808: a study of stellar activity modelling's impact on planet detection [2102.03387](entry.id) ## Abstract We present a comprehensive analysis of 10 years of HARPS radial velocities of the K2V dwarf star HD 13808, which has previously been reported to host two unconfirmed planet candidates. We use the state-of-the-art nested sampling algorithm PolyChord to compare a wide variety of stellar activity models, including simple models exploiting linear correlations between RVs and stellar activity indicators, harmonic models for the activity signals, and a more sophisticated Gaussian process regression model. We show that the use of overly-simplistic stellar activity models that are not well-motivated physically can lead to spurious `detections' of planetary signals that are almost certainly not real. We also reveal some difficulties inherent in parameter and model inference in cases where multiple planetary signals may be present. Our study thus underlines the importance both of exploring a variety of competing models and of understanding the limitations and precision settings of one's sampling algorithm. We also show that at least in the case of HD 13808, we always arrive at consistent conclusions about two particular signals present in the RV, regardless of the stellar activity model we adopt; these two signals correspond to the previously-reported though unconfirmed planet candidate signals. Given the robustness and precision with which we can characterize these two signals, we deem them secure planet detections. In particular, we find two planets orbiting HD 13808 at distances of 0.11, 0.26 AU with periods of 14.2, 53.8 d, and minimum masses of 11, 10 Earth masses. ## Authors E. Ahrer, D. Queloz, V. M. Rajpaul, D. Ségransan, F. Bouchy, R. Hall, W. Handley, C. Lovis, M. Mayor, A. Mortier, F. Pepe, S. Thompson, S. Udry, N. Unger ## Published 2021-02-05T19:21:00Z # Nonlinear Hamiltonian analysis of new quadratic torsion theories Part I. Cases with curvature-free constraints [2101.02645](entry.id) ## Abstract It was recently found that, when linearised in the absence of matter, 58 cases of the general gravitational theory with quadratic curvature and torsion are (i) free from ghosts and tachyons and (ii) power-counting renormalisable. We inspect the nonlinear Hamiltonian structure of the eight cases whose primary constraints do not depend on the curvature tensor. We confirm the particle spectra and unitarity of all these theories in the linear regime. We uncover qualitative dynamical changes in the nonlinear regimes of all eight cases, suggesting at least a broken gauge symmetry, and possibly the activation of negative kinetic energy spin-parity sectors and acausal behaviour. Two of the cases propagate a pair of massless modes at the linear level, and were interesting as candidate theories of gravity. However, we identify these modes with vector excitations, rather than the tensor polarisations of the graviton. Moreover, we show that these theories do not support a viable cosmological background. ## Authors W. E. V. Barker, A. N. Lasenby, M. P. Hobson, W. J. Handley ## Published 2021-01-07T17:33:31Z # Quantifying Ionospheric Effects on Global 21-cm Observations [2011.10517](entry.id) ## Abstract We modelled the two major layer of Earth's ionosphere, the F-layer and the D-layer, by a simplified spatial model with temporal variance to study the chromatic ionospheric effects on global 21-cm observations. From the analyses, we found that the magnitude of the ionospheric disruptions due to ionospheric refraction and absorption can be greater than the expected global 21-cm signal, and the variation of its magnitude can differ, depending on the ionospheric conditions. Within the parameter space adopted in the model, the shape of the global 21-cm signal is distorted after propagating through the ionosphere, while its amplitude is weakened. It is observed that the ionospheric effects do not cancel out over time, and thus should be accounted for in the foreground calibration at each timestep to account for the chromaticity introduced by the ionosphere. ## Authors Emma Shen, Dominic Anstey, Eloy de Lera Acedo, Anastasia Fialkov, Will Handley ## Published 2020-11-20T17:23:09Z # Planck 2018 results. IV. Diffuse component separation [1807.06208](entry.id) ## Abstract We present full-sky maps of the cosmic microwave background (CMB) and polarized synchrotron and thermal dust emission, derived from the third set of Planck frequency maps. These products have significantly lower contamination from instrumental systematic effects than previous versions. The methodologies used to derive these maps follow those described in earlier papers, adopting four methods (Commander, NILC, SEVEM, and SMICA) to extract the CMB component, as well as three methods (Commander, GNILC, and SMICA) to extract astrophysical components. Our revised CMB temperature maps agree with corresponding products in the Planck 2015 delivery, whereas the polarization maps exhibit significantly lower large-scale power, reflecting the improved data processing described in companion papers; however, the noise properties of the resulting data products are complicated, and the best available end-to-end simulations exhibit relative biases with respect to the data at the few percent level. Using these maps, we are for the first time able to fit the spectral index of thermal dust independently over 3 degree regions. We derive a conservative estimate of the mean spectral index of polarized thermal dust emission of beta_d = 1.55 +/- 0.05, where the uncertainty marginalizes both over all known systematic uncertainties and different estimation techniques. For polarized synchrotron emission, we find a mean spectral index of beta_s = -3.1 +/- 0.1, consistent with previously reported measurements. We note that the current data processing does not allow for construction of unbiased single-bolometer maps, and this limits our ability to extract CO emission and correlated components. The foreground results for intensity derived in this paper therefore do not supersede corresponding Planck 2015 products. For polarization the new results supersede the corresponding 2015 products in all respects. ## Authors Planck Collaboration, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, E. Calabrese, J. -F. Cardoso, J. Carron, B. Casaponsa, A. Challinor, L. P. L. Colombo, C. Combet, B. P. Crill, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, C. Dickinson, J. M. Diego, S. Donzelli, O. Doré, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, E. Falgarone, R. Fernandez-Cobos, F. Finelli, F. Forastieri, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, W. Handley, F. K. Hansen, G. Helou, D. Herranz, Z. Huang, A. H. Jaffe, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, P. Natoli, F. Oppizzi, L. Pagano, D. Paoletti, B. Partridge, M. Peel, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, D. S. Seljebotn, C. Sirignano, L. D. Spencer, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, H. Thommesen, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2018-07-17T04:05:06Z # Planck 2018 results. V. CMB power spectra and likelihoods [1907.12875](entry.id) ## Abstract This paper describes the 2018 Planck CMB likelihoods, following a hybrid approach similar to the 2015 one, with different approximations at low and high multipoles, and implementing several methodological and analysis refinements. With more realistic simulations, and better correction and modelling of systematics, we can now make full use of the High Frequency Instrument polarization data. The low-multipole 100x143 GHz EE cross-spectrum constrains the reionization optical-depth parameter $\tau$ to better than 15% (in combination with with the other low- and high-$\ell$ likelihoods). We also update the 2015 baseline low-$\ell$ joint TEB likelihood based on the Low Frequency Instrument data, which provides a weaker $\tau$ constraint. At high multipoles, a better model of the temperature-to-polarization leakage and corrections for the effective calibrations of the polarization channels (polarization efficiency or PE) allow us to fully use the polarization spectra, improving the constraints on the $\Lambda$CDM parameters by 20 to 30% compared to TT-only constraints. Tests on the modelling of the polarization demonstrate good consistency, with some residual modelling uncertainties, the accuracy of the PE modelling being the main limitation. Using our various tests, simulations, and comparison between different high-$\ell$ implementations, we estimate the consistency of the results to be better than the 0.5$\sigma$ level. Minor curiosities already present before (differences between $\ell$<800 and $\ell$>800 parameters or the preference for more smoothing of the $C_\ell$ peaks) are shown to be driven by the TT power spectrum and are not significantly modified by the inclusion of polarization. Overall, the legacy Planck CMB likelihoods provide a robust tool for constraining the cosmological model and represent a reference for future CMB observations. (Abridged) ## Authors Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, J. Carron, B. Casaponsa, A. Challinor, H. C. Chiang, L. P. L. Colombo, C. Combet, B. P. Crill, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, S. Dusini, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, R. Fernandez-Cobos, F. Finelli, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, Y. Giraud-Héraud, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Lilley, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. Millea, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, P. Natoli, H. U. Nørgaard-Nielsen, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, H. V. Peiris, F. Perrotta, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, E. P. S. Shellard, C. Sirignano, G. Sirri, L. D. Spencer, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2019-07-30T13:11:32Z # Planck intermediate results. LV. Reliability and thermal properties of high-frequency sources in the Second Planck Catalogue of Compact Sources [2009.06333](entry.id) ## Abstract We describe an extension of the most recent version of the Planck Catalogue of Compact Sources (PCCS2), produced using a new multi-band Bayesian Extraction and Estimation Package (BeeP). BeeP assumes that the compact sources present in PCCS2 at 857 GHz have a dust-like spectral energy distribution, which leads to emission at both lower and higher frequencies, and adjusts the parameters of the source and its SED to fit the emission observed in Planck's three highest frequency channels at 353, 545, and 857 GHz, as well as the IRIS map at 3000 GHz. In order to reduce confusion regarding diffuse cirrus emission, BeeP's data model includes a description of the background emission surrounding each source, and it adjusts the confidence in the source parameter extraction based on the statistical properties of the spatial distribution of the background emission. BeeP produces the following three new sets of parameters for each source: (a) fits to a modified blackbody (MBB) thermal emission model of the source; (b) SED-independent source flux densities at each frequency considered; and (c) fits to an MBB model of the background in which the source is embedded. BeeP also calculates, for each source, a reliability parameter, which takes into account confusion due to the surrounding cirrus. We define a high-reliability subset (BeeP/base), containing 26 083 sources (54.1 per cent of the total PCCS2 catalogue), the majority of which have no information on reliability in the PCCS2. The results of the BeeP extension of PCCS2, which are made publicly available via the PLA, will enable the study of the thermal properties of well-defined samples of compact Galactic and extra-galactic dusty sources. ## Authors Planck Collaboration, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, F. R. Bouchet, C. Burigana, E. Calabrese, P. Carvalho, H. C. Chiang, B. P. Crill, F. Cuttaia, A. de Rosa, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, J. M. Diego, X. Dupac, S. Dusini, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, R. Fernandez-Cobos, F. Finelli, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, K. Ganga, M. Gerbino, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, M. Hobson, Z. Huang, W. C. Jones, E. Keihänen, R. Keskitalo, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, P. B. Lilje, V. Lindholm, M. López-Caniego, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, N. Mandolesi, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, M. Migliaccio, D. Molinari, A. Moneti, L. Montier, G. Morgante, P. Natoli, D. Paoletti, B. Partridge, F. Perrotta, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, G. Roudier, B. Ruiz-Granados, M. Savelainen, D. Scott, G. Sirri, L. D. Spencer, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2020-09-14T11:42:25Z # Planck 2018 results. VII. Isotropy and Statistics of the CMB [1906.02552](entry.id) ## Abstract Analysis of the Planck 2018 data set indicates that the statistical properties of the cosmic microwave background (CMB) temperature anisotropies are in excellent agreement with previous studies using the 2013 and 2015 data releases. In particular, they are consistent with the Gaussian predictions of the $\Lambda$CDM cosmological model, yet also confirm the presence of several so-called "anomalies" on large angular scales. The novelty of the current study, however, lies in being a first attempt at a comprehensive analysis of the statistics of the polarization signal over all angular scales, using either maps of the Stokes parameters, $Q$ and $U$, or the $E$-mode signal derived from these using a new methodology (which we describe in an appendix). Although remarkable progress has been made in reducing the systematic effects that contaminated the 2015 polarization maps on large angular scales, it is still the case that residual systematics (and our ability to simulate them) can limit some tests of non-Gaussianity and isotropy. However, a detailed set of null tests applied to the maps indicates that these issues do not dominate the analysis on intermediate and large angular scales (i.e., $\ell \lesssim 400$). In this regime, no unambiguous detections of cosmological non-Gaussianity, or of anomalies corresponding to those seen in temperature, are claimed. Notably, the stacking of CMB polarization signals centred on the positions of temperature hot and cold spots exhibits excellent agreement with the $\Lambda$CDM cosmological model, and also gives a clear indication of how Planck provides state-of-the-art measurements of CMB temperature and polarization on degree scales. ## Authors Planck Collaboration, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, B. Casaponsa, H. C. Chiang, L. P. L. Colombo, C. Combet, D. Contreras, B. P. Crill, P. de Bernardis, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, R. Fernandez-Cobos, F. Finelli, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. R. Meinhold, A. Mennella, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, P. Natoli, L. Pagano, D. Paoletti, B. Partridge, F. Perrotta, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Savelainen, D. Scott, E. P. S. Shellard, C. Sirignano, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, L. Valenziano, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, A. Zacchei, J. P. Zibin, A. Zonca ## Published 2019-06-06T12:37:08Z # Planck intermediate results. LVI. Detection of the CMB dipole through modulation of the thermal Sunyaev-Zeldovich effect: Eppur si muove II [2003.12646](entry.id) ## Abstract The largest temperature anisotropy in the cosmic microwave background (CMB) is the dipole, which has been measured with increasing accuracy for more than three decades, particularly with the Planck satellite. The simplest interpretation of the dipole is that it is due to our motion with respect to the rest frame of the CMB. Since current CMB experiments infer temperature anisotropies from angular intensity variations, the dipole modulates the temperature anisotropies with the same frequency dependence as the thermal Sunyaev-Zeldovich (tSZ) effect. We present the first, and significant, detection of this signal in the tSZ maps and find that it is consistent with direct measurements of the CMB dipole, as expected. The signal contributes power in the tSZ maps, which is modulated in a quadrupolar pattern, and we estimate its contribution to the tSZ bispectrum, noting that it contributes negligible noise to the bispectrum at relevant scales. ## Authors Planck Collaboration, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, F. R. Bouchet, C. Burigana, E. Calabrese, J. -F. Cardoso, B. Casaponsa, H. C. Chiang, C. Combet, D. Contreras, B. P. Crill, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, X. Dupac, T. A. Enßlin, H. K. Eriksen, R. Fernandez-Cobos, F. Finelli, M. Frailis, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, J. González-Nuevo, K. M. Górski, A. Gruppuso, J. E. Gudmundsson, W. Handley, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, J. -M. Lamarre, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, J. F. Macías-Pérez, D. Maino, N. Mandolesi, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, A. Mennella, M. Migliaccio, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, P. Natoli, L. Pagano, D. Paoletti, F. Perrotta, V. Pettorino, F. Piacentini, G. Polenta, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Savelainen, D. Scott, C. Sirignano, G. Sirri, L. D. Spencer, R. M. Sullivan, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2020-03-27T21:43:37Z # Mapping Poincaré gauge cosmology to Horndeski theory for emergent dark energy [2006.03581](entry.id) ## Abstract The ten-parameter, quadratic Poincar\'e gauge theory of gravity is a plausible alternative to general relativity. We show that the rich background cosmology of the gauge theory is described by a non-canonical bi-scalar-tensor theory in the Jordan frame: the `metrical analogue'. This provides a unified framework for future investigation by the broader community. For many parameter choices, the non-canonical term reduces to a Cuscuton field of the form $\smash{\sqrt{|X^{\phi\phi}|}}$. The Einstein-Cartan-Kibble-Sciama theory maps to a pure quadratic Cuscuton, whereas the teleparallel theory maps to the Einstein-Hilbert Lagrangian. We apply the metrical analogue to novel unitary and power-counting-renormalisable cases of Poincar\'e gauge theory. These theories support the concordance $\Lambda$CDM background cosmology up to an optional, effective dark radiation component, we explain this behaviour in terms of a stalled Cuscuton. We also obtain two dark energy solutions from one of these cases: accelerated expansion from a negative bare cosmological constant whose magnitude is screened, and emergent dark energy to replace vanishing bare cosmological constant in $\Lambda$CDM. ## Authors W. E. V. Barker, A. N. Lasenby, M. P. Hobson, W. J. Handley ## Published 2020-06-05T17:54:04Z # Nested sampling cross-checks using order statistics [2006.03371](entry.id) ## Abstract Nested sampling (NS) is an invaluable tool in data analysis in modern astrophysics, cosmology, gravitational wave astronomy and particle physics. We identify a previously unused property of NS related to order statistics: the insertion indexes of new live points into the existing live points should be uniformly distributed. This observation enabled us to create a novel cross-check of single NS runs. The tests can detect when an NS run failed to sample new live points from the constrained prior and plateaus in the likelihood function, which break an assumption of NS and thus leads to unreliable results. We applied our cross-check to NS runs on toy functions with known analytic results in 2 - 50 dimensions, showing that our approach can detect problematic runs on a variety of likelihoods, settings and dimensions. As an example of a realistic application, we cross-checked NS runs performed in the context of cosmological model selection. Since the cross-check is simple, we recommend that it become a mandatory test for every applicable NS run. ## Authors Andrew Fowlie, Will Handley, Liangliang Su ## Published 2020-06-05T11:19:03Z # Global Analysis of the TRAPPIST Ultra-Cool Dwarf Transit Survey [2007.07278](entry.id) ## Abstract We conducted a global analysis of the TRAPPIST Ultra-Cool Dwarf Transit Survey - a prototype of the SPECULOOS transit search conducted with the TRAPPIST-South robotic telescope in Chile from 2011 to 2017 - to estimate the occurrence rate of close-in planets such as TRAPPIST-1b orbiting ultra-cool dwarfs. For this purpose, the photometric data of 40 nearby ultra-cool dwarfs were reanalysed in a self-consistent and fully automated manner starting from the raw images. The pipeline developed specifically for this task generates differential light curves, removes non-planetary photometric features and stellar variability, and searches for transits. It identifies the transits of TRAPPIST-1b and TRAPPIST-1c without any human intervention. To test the pipeline and the potential output of similar surveys, we injected planetary transits into the light curves on a star-by-star basis and tested whether the pipeline is able to detect them. The achieved photometric precision enables us to identify Earth-sized planets orbiting ultra-cool dwarfs as validated by the injection tests. Our planet-injection simulation further suggests a lower limit of 10 per cent on the occurrence rate of planets similar to TRAPPIST-1b with a radius between 1 and 1.3 $R_\oplus$ and the orbital period between 1.4 and 1.8 days. ## Authors F. Lienhard, D. Queloz, M. Gillon, A. Burdanov, L. Delrez, E. Ducrot, W. Handley, E. Jehin, C. A. Murray, A. H. M. J. Triaud, E. Gillen, A. Mortier, B. V. Rackham ## Published 2020-07-14T18:16:31Z # Addressing $H_0$ tension with emergent dark radiation in unitary gravity [2003.02690](entry.id) ## Abstract We propose a one-parameter extension to $\Lambda$CDM, expected to strongly affect cosmological tensions. An effective dark radiation component in the early universe redshifts away as hot dark matter, then quintessence, tracking the dominant equation-of-state parameter and leaving a falsifiable torsion field in the current epoch. This picture results from a new Poincar\'{e} gauge theory (PGT), one of the most promising among the latest batch of 58 PGTs found to be both power-counting renormalisable and free from ghosts and tachyons. We systematically categorise the cosmologies of 33 of these PGTs, as special cases of the most general parity-preserving, Ostrogradsky-stable PGT with a purely Yang-Mills action. The theory we consider contains two propagating massless gravitons, which may be $J^P=2^+$ (long-range gravitation and gravitational waves). A conspiracy among the coupling constants eliminates the spatial curvature $k\in\{\pm 1,0\}$ from the field equations. We show that this `$k$-screening' is not restricted to conformal gravity theories. The flat Friedmann equations are then emergent, with potentially tension-resolving freedom at the early scale-invariant epoch that reliably gives way to an attractor-like state of modern $\Lambda$CDM evolution. We compare with related theories and promising special cases, such as $k$-screened theories with negative-definite effective $k$, and more traditional theories with effective $\Lambda$ and a $J^P=0^-$ massive graviton (dark matter candidate). As a bonus, we analyse similarly constrained actions in the new extended Weyl gauge theory (eWGT). We show that in cosmology, PGT and eWGT span exactly the same classical phenomenology up to a linear map between their coupling constants, hinting at a deeper relationship between the two. ## Authors W. E. V. Barker, A. N. Lasenby, M. P. Hobson, W. J. Handley ## Published 2020-03-05T14:59:08Z # Dense output for highly oscillatory numerical solutions [2007.05013](entry.id) ## Abstract We present a method to construct a continuous extension (otherwise known as dense output) for a numerical routine in the special case of the numerical solution being a scalar-valued function exhibiting rapid oscillations. Such cases call for numerical routines that make use of the known global behaviour of the solution, one example being methods using asymptotic expansions to forecast the solution at each step of the independent variable. An example is oscode, numerical routine which uses the Wentzel-Kramers-Brillouin (WKB) approximation when the solution oscillates rapidly and otherwise behaves as a Runge-Kutta (RK) solver. Polynomial interpolation is not suitable for producing the solution at an arbitrary point mid-step, since efficient numerical methods based on the WKB approximation will step through multiple oscillations in a single step. Instead we construct the continuous solution by extending the numerical quadrature used in computing a WKB approximation of the solution with no additional evaluations of the differential equation or terms within, and provide an error estimate on this dense output. Finally, we draw attention to previous work on the continuous extension of Runge-Kutta formulae, and construct an extension to a RK method based on Gauss--Lobatto quadrature nodes, thus describing how to generate dense output from each of the methods underlying oscode. ## Authors F. J. Agocs, M. P. Hobson, W. J. Handley, A. N. Lasenby ## Published 2020-07-09T18:11:45Z # Planck intermediate results. LVII. Joint Planck LFI and HFI data processing [2007.04997](entry.id) ## Abstract We present the NPIPE processing pipeline, which produces calibrated frequency maps in temperature and polarization from data from the Planck Low Frequency Instrument (LFI) and High Frequency Instrument (HFI) using high-performance computers. NPIPE represents a natural evolution of previous Planck analysis efforts, and combines some of the most powerful features of the separate LFI and HFI analysis pipelines. The net effect of the improvements is lower levels of noise and systematics in both frequency and component maps at essentially all angular scales, as well as notably improved internal consistency between the various frequency channels. Based on the NPIPE maps, we present the first estimate of the Solar dipole determined through component separation across all nine Planck frequencies. The amplitude is ($3366.6 \pm 2.7$)$\mu$K, consistent with, albeit slightly higher than, earlier estimates. From the large-scale polarization data, we derive an updated estimate of the optical depth of reionization of $\tau = 0.051 \pm 0.006$, which appears robust with respect to data and sky cuts. There are 600 complete signal, noise and systematics simulations of the full-frequency and detector-set maps. As a Planck first, these simulations include full time-domain processing of the beam-convolved CMB anisotropies. The release of NPIPE maps and simulations is accompanied with a complete suite of raw and processed time-ordered data and the software, scripts, auxiliary data, and parameter files needed to improve further on the analysis and to run matching simulations. ## Authors Planck Collaboration, Y. Akrami, K. J. Andersen, M. Ashdown, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, C. Burigana, R. C. Butler, E. Calabrese, B. Casaponsa, H. C. Chiang, L. P. L. Colombo, C. Combet, B. P. Crill, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, X. Dupac, H. K. Eriksen, R. Fernandez-Cobos, F. Finelli, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, A. Gruppuso, J. E. Gudmundsson, W. Handley, G. Helou, D. Herranz, S. R. Hildebrandt, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, M. Liguori, P. B. Lilje, M. Lilley, V. Lindholm, M. López-Caniego, P. M. Lubin, J. F. Macías-Pérez, D. Maino, N. Mandolesi, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. R. Meinhold, A. Mennella, M. Migliaccio, S. Mitra, D. Molinari, L. Montier, G. Morgante, A. Moss, P. Natoli, D. Paoletti, B. Partridge, G. Patanchon, D. Pearson, T. J. Pearson, F. Perrotta, F. Piacentini, G. Polenta, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Savelainen, D. Scott, C. Sirignano, G. Sirri, L. D. Spencer, A. -S. Suur-Uski, T. L. Svalheim, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Terenzi, H. Thommesen, L. Toffolatti, M. Tomasi, M. Tristram, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2020-07-09T18:00:02Z # Compromise-free Bayesian neural networks [2004.12211](entry.id) ## Abstract We conduct a thorough analysis of the relationship between the out-of-sample performance and the Bayesian evidence (marginal likelihood) of Bayesian neural networks (BNNs), as well as looking at the performance of ensembles of BNNs, both using the Boston housing dataset. Using the state-of-the-art in nested sampling, we numerically sample the full (non-Gaussian and multimodal) network posterior and obtain numerical estimates of the Bayesian evidence, considering network models with up to 156 trainable parameters. The networks have between zero and four hidden layers, either $\tanh$ or $ReLU$ activation functions, and with and without hierarchical priors. The ensembles of BNNs are obtained by determining the posterior distribution over networks, from the posterior samples of individual BNNs re-weighted by the associated Bayesian evidence values. There is good correlation between out-of-sample performance and evidence, as well as a remarkable symmetry between the evidence versus model size and out-of-sample performance versus model size planes. Networks with $ReLU$ activation functions have consistently higher evidences than those with $\tanh$ functions, and this is reflected in their out-of-sample performance. Ensembling over architectures acts to further improve performance relative to the individual BNNs. ## Authors Kamran Javid, Will Handley, Mike Hobson, Anthony Lasenby ## Published 2020-04-25T19:12:56Z # Quantum initial conditions for inflation and canonical invariance [2002.07042](entry.id) ## Abstract We investigate the transformation of initial conditions for primordial curvature perturbations under two types of transformations of the associated action: simultaneous redefinition of time and the field to be quantised, and the addition of surface terms. The latter encompasses all canonical transformations, whilst the time- and field-redefinition is a distinct, non-canonical transformation since the initial and destination systems use different times. Actions related to each other via such transformations yield identical equations of motion and preserve the commutator structure. They further preserve the time-evolution of expectation values of quantum operators unless the vacuum state also changes under the transformation. These properties suggest that it is of interest to investigate vacuum prescriptions that also remain unchanged under canonical transformations. We find that initial conditions derived via minimising the vacuum expectation value of the Hamiltonian and those obtained using the Danielsson vacuum prescription are not invariant under these transformations, whereas those obtained by minimising the local energy density are. We derive the range of physically distinct initial conditions obtainable by Hamiltonian diagonalisation, and illustrate their effect on the scalar primordial power spectrum and the Cosmic Microwave Background under the just enough inflation model. We also generalise the analogy between the dynamics of a quantum scalar field on a curved, time-dependent spacetime and the gauge-invariant curvature perturbation. We argue that the invariance of the vacuum prescription obtained by minimising the renormalised stress--energy tensor should make it the preferred procedure for setting initial conditions for primordial perturbations. All other procedures reviewed in this work yield ambiguous initial conditions, which is problematic both in theory and practice. ## Authors F. J. Agocs, L. T. Hergt, W. J. Handley, A. N. Lasenby, M. P. Hobson ## Published 2020-02-14T10:49:33Z # Static energetics in gravity [1811.09844](entry.id) ## Abstract A stress-energy tensor for linear gravity adapted to the harmonic gauge was recently proposed by Butcher, Hobson and Lasenby. By removing gauge constraints and imposing full metrical GR, we find a natural generalisation to the pseudotensor of Einstein. M{\o}ller's pseudotensor is an alternative to that of Einstein formulated using tetrads. We obtain the pseudotensor of M{\o}ller for gauge theory gravity (GTG) using a variational approach, identifying a potentially interesting recipe for constructing conserved currents in that theory. We show that in static, spherical spacetimes with a central gravitational mass M{\o}ller's pseudotensor describes gravitational stress-energy as if the gravitational potential were a scalar (i.e. Klein-Gordon) field coupled to a gravitational mass density on the Minkowski background. The old Newtonian formula successfully describes the potential of even strong fields in this picture. The Newtonian limit of this effect was previously observed in the tensor of Butcher; we recover a local virial theorem in this limit. We demonstrate using the `Schwarzschild star' solution for an incompressible perfect fluid ball. ## Authors William E V Barker, Anthony N Lasenby, Michael P Hobson, William J Handley ## Published 2018-11-24T14:27:11Z # Beyond the Runge-Kutta-Wentzel-Kramers-Brillouin method [1907.11638](entry.id) ## Abstract We explore higher-dimensional generalizations of the Runge-Kutta-Wentzel-Kramers-Brillouin method for integrating coupled systems of first-order ordinary differential equations with highly oscillatory solutions. Such methods could improve the performance and adaptability of the codes which are used to compute numerical solutions to the Einstein-Boltzmann equations. We test Magnus expansion-based methods on the Einstein-Boltzmann equations for a simple universe model dominated by photons with a small amount of cold dark matter. The Magnus expansion methods achieve an increase in run speed of about 50% compared to a standard Runge-Kutta integration method. A comparison of approximate solutions derived from the Magnus expansion and the Wentzel-Kramers-Brillouin (WKB) method implies the two are distinct mathematical approaches. Simple Magnus expansion solutions show inferior long range accuracy compared to WKB. However we also demonstrate how one can improve on the standard Magnus approach to obtain a new "Jordan-Magnus" method. This has a WKB-like performance on simple two-dimensional systems, although its higher-dimensional generalization remains elusive. ## Authors Jamie Bamber, Will Handley ## Published 2019-07-26T15:50:05Z # Primordial power spectra for curved inflating universes [1907.08524](entry.id) ## Abstract Exact numerical primordial primordial power spectra are computed and plotted for the for the best-fit Planck 2018 curved universe parameters. It is found that the spectra have generic cut-offs and oscillations within the observable window for the level of curvature allowed by current CMB measurements and provide a better fit to current data. Derivations for the Mukhanov-Sasaki equation for curved universes are presented and analysed, and theoretical implications for the quantum and classical initial conditions for inflation are discussed within the curved regime. ## Authors Will Handley ## Published 2019-07-19T14:20:56Z # An efficient method for solving highly oscillatory ordinary differential equations with applications to physical systems [1906.01421](entry.id) ## Abstract We present a novel numerical routine (oscode) with a C++ and Python interface for the efficient solution of one-dimensional, second-order, ordinary differential equations with rapidly oscillating solutions. The method is based on a Runge-Kutta-like stepping procedure that makes use of the Wentzel-Kramers-Brillouin (WKB) approximation to skip regions of integration where the characteristic frequency varies slowly. In regions where this is not the case, the method is able to switch to a made-to-measure Runge-Kutta integrator that minimises the total number of function evaluations. We demonstrate the effectiveness of the method with example solutions of the Airy equation and an equation exhibiting a burst of oscillations, discussing the error properties of the method in detail. We then show the method applied to physical systems. First, the one-dimensional, time-independent Schr\"odinger equation is solved as part of a shooting method to search for the energy eigenvalues for a potential with quartic anharmonicity. Then, the method is used to solve the Mukhanov-Sasaki equation describing the evolution of cosmological perturbations, and the primordial power spectrum of the perturbations is computed in different cosmological scenarios. We compare the performance of our solver in calculating a primordial power spectrum of scalar perturbations to that of BINGO, an efficient code specifically designed for such applications. ## Authors F. J. Agocs, W. J. Handley, A. N. Lasenby, M. P. Hobson ## Published 2019-05-30T18:00:00Z # Planck 2018 results. I. Overview and the cosmological legacy of Planck [1807.06205](entry.id) ## Abstract The European Space Agency's Planck satellite, which was dedicated to studying the early Universe and its subsequent evolution, was launched on 14 May 2009. It scanned the microwave and submillimetre sky continuously between 12 August 2009 and 23 October 2013, producing deep, high-resolution, all-sky maps in nine frequency bands from 30 to 857GHz. This paper presents the cosmological legacy of Planck, which currently provides our strongest constraints on the parameters of the standard cosmological model and some of the tightest limits available on deviations from that model. The 6-parameter LCDM model continues to provide an excellent fit to the cosmic microwave background data at high and low redshift, describing the cosmological information in over a billion map pixels with just six parameters. With 18 peaks in the temperature and polarization angular power spectra constrained well, Planck measures five of the six parameters to better than 1% (simultaneously), with the best-determined parameter (theta_*) now known to 0.03%. We describe the multi-component sky as seen by Planck, the success of the LCDM model, and the connection to lower-redshift probes of structure formation. We also give a comprehensive summary of the major changes introduced in this 2018 release. The Planck data, alone and in combination with other probes, provide stringent constraints on our models of the early Universe and the large-scale structure within which all astrophysical objects form and evolve. We discuss some lessons learned from the Planck mission, and highlight areas ripe for further experimental advances. ## Authors Planck Collaboration, Y. Akrami, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, R. Battye, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, J. Carron, B. Casaponsa, A. Challinor, H. C. Chiang, L. P. L. Colombo, C. Combet, D. Contreras, B. P. Crill, F. Cuttaia, P. de Bernardis, G. de Zotti, J. Delabrouille, J. -M. Delouis, F. -X. Désert, E. Di Valentino, C. Dickinson, J. M. Diego, S. Donzelli, O. Doré, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, E. Falgarone, Y. Fantaye, J. Fergusson, R. Fernandez-Cobos, F. Finelli, F. Forastieri, M. Frailis, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, G. Helou, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, L. Knox, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, M. Langer, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, J. P. Leahy, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Lilley, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. D. Meerburg, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. Millea, S. Mitra, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, S. Mottet, M. Münchmeyer, P. Natoli, H. U. Nørgaard-Nielsen, C. A. Oxborrow, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, T. J. Pearson, M. Peel, H. V. Peiris, F. Perrotta, V. Pettorino, F. Piacentini, L. Polastri, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, E. P. S. Shellard, M. Shiraishi, C. Sirignano, G. Sirri, L. D. Spencer, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Terenzi, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, L. Vibert, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, M. White, S. D. M. White, A. Zacchei, A. Zonca ## Published 2018-07-17T04:05:03Z # Quantifying tensions in cosmological parameters: Interpreting the DES evidence ratio [1902.04029](entry.id) ## Abstract We provide a new interpretation for the Bayes factor combination used in the Dark Energy Survey (DES) first year analysis to quantify the tension between the DES and Planck datasets. The ratio quantifies a Bayesian confidence in our ability to combine the datasets. This interpretation is prior-dependent, with wider prior widths boosting the confidence. We therefore propose that if there are any reasonable priors which reduce the confidence to below unity, then we cannot assert that the datasets are compatible. Computing the evidence ratios for the DES first year analysis and Planck, given that narrower priors drop the confidence to below unity, we conclude that DES and Planck are, in a Bayesian sense, incompatible under LCDM. Additionally we compute ratios which confirm the consensus that measurements of the acoustic scale by the Baryon Oscillation Spectroscopic Survey (SDSS) are compatible with Planck, whilst direct measurements of the acceleration rate of the Universe by the SHOES collaboration are not. We propose a modification to the Bayes ratio which removes the prior dependency using Kullback-Leibler divergences, and using this statistical test find Planck in strong tension with SHOES, in moderate tension with DES, and in no tension with SDSS. We propose this statistic as the optimal way to compare datasets, ahead of the next DES data releases, as well as future surveys. Finally, as an element of these calculations, we introduce in a cosmological setting the Bayesian model dimensionality, which is a parameterisation-independent measure of the number of parameters that a given dataset constrains. ## Authors Will Handley, Pablo Lemos ## Published 2019-02-11T18:11:13Z # Quantifying dimensionality: Bayesian cosmological model complexities [1903.06682](entry.id) ## Abstract We demonstrate a measure for the effective number of parameters constrained by a posterior distribution in the context of cosmology. In the same way that the mean of the Shannon information (i.e. the Kullback-Leibler divergence) provides a measure of the strength of constraint between prior and posterior, we show that the variance of the Shannon information gives a measure of dimensionality of constraint. We examine this quantity in a cosmological context, applying it to likelihoods derived from Cosmic Microwave Background, large scale structure and supernovae data. We show that this measure of Bayesian model dimensionality compares favourably both analytically and numerically in a cosmological context with the existing measure of model complexity used in the literature. ## Authors Will Handley, Pablo Lemos ## Published 2019-03-15T17:27:32Z # Bayesian inflationary reconstructions from Planck 2018 data [1908.00906](entry.id) ## Abstract We present three non-parametric Bayesian primordial reconstructions using Planck 2018 polarization data: linear spline primordial power spectrum reconstructions, cubic spline inflationary potential reconstructions and sharp-featured primordial power spectrum reconstructions. All three methods conditionally show hints of an oscillatory feature in the primordial power spectrum in the multipole range $\ell\sim20$ to $\ell\sim50$, which is to some extent preserved upon marginalization. We find no evidence for deviations from a pure power law across a broad observable window ($50\lesssim\ell\lesssim2000$), but find that parameterizations are preferred which are able to account for lack of resolution at large angular scales due to cosmic variance, and at small angular scales due to Planck instrument noise. Furthermore, the late-time cosmological parameters are unperturbed by these extensions to the primordial power spectrum. This work is intended to provide a background and give more details of the Bayesian primordial reconstruction work found in the Planck 2018 papers. ## Authors Will J. Handley, Anthony N. Lasenby, Hiranya V. Peiris, Michael P. Hobson ## Published 2019-08-02T15:27:47Z # Quantifying Suspiciousness Within Correlated Data Sets [1910.07820](entry.id) ## Abstract We propose a principled Bayesian method for quantifying tension between correlated datasets with wide uninformative parameter priors. This is achieved by extending the Suspiciousness statistic, which is insensitive to priors. Our method uses global summary statistics, and as such it can be used as a diagnostic for internal consistency. We show how our approach can be combined with methods that use parameter space and data space to identify the existing internal discrepancies. As an example, we use it to test the internal consistency of the KiDS-450 data in 4 photometric redshift bins, and to recover controlled internal discrepancies in simulated KiDS data. We propose this as a diagnostic of internal consistency for present and future cosmological surveys, and as a tension metric for data sets that have non-negligible correlation, such as LSST and Euclid. ## Authors Pablo Lemos, Fabian Köhlinger, Will Handley, Benjamin Joachimi, Lorne Whiteway, Ofer Lahav ## Published 2019-10-17T10:48:22Z # Curvature tension: evidence for a closed universe [1908.09139](entry.id) ## Abstract The curvature parameter tension between Planck 2018, cosmic microwave background lensing, and baryon acoustic oscillation data is measured using the suspiciousness statistic to be 2.5 to 3$\sigma$. Conclusions regarding the spatial curvature of the universe which stem from the combination of these data should therefore be viewed with suspicion. Without CMB lensing or BAO, Planck 2018 has a moderate preference for closed universes, with Bayesian betting odds of over 50:1 against a flat universe, and over 2000:1 against an open universe. ## Authors Will Handley ## Published 2019-08-24T13:56:59Z # fgivenx: A Python package for functional posterior plotting [1908.01711](entry.id) ## Abstract fgivenx is a Python package for functional posterior plotting, currently used in astronomy, but will be of use to scientists performing any Bayesian analysis which has predictive posteriors that are functions. The source code for fgivenx is available on GitHub at https://github.com/williamjameshandley/fgivenx ## Authors Will Handley ## Published 2019-08-02T15:30:12Z # Planck 2018 results. X. Constraints on inflation [1807.06211](entry.id) ## Abstract We report on the implications for cosmic inflation of the 2018 Release of the Planck CMB anisotropy measurements. The results are fully consistent with the two previous Planck cosmological releases, but have smaller uncertainties thanks to improvements in the characterization of polarization at low and high multipoles. Planck temperature, polarization, and lensing data determine the spectral index of scalar perturbations to be $n_\mathrm{s}=0.9649\pm 0.0042$ at 68% CL and show no evidence for a scale dependence of $n_\mathrm{s}.$ Spatial flatness is confirmed at a precision of 0.4% at 95% CL with the combination with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio, $r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field inflationary models with Einstein gravity, these results imply that: (a) slow-roll models with a concave potential, $V" (\phi) < 0,$ are increasingly favoured by the data; and (b) two different methods for reconstructing the inflaton potential find no evidence for dynamics beyond slow roll. Non-parametric reconstructions of the primordial power spectrum consistently confirm a pure power law. A complementary analysis also finds no evidence for theoretically motivated parameterized features in the Planck power spectrum, a result further strengthened for certain oscillatory models by a new combined analysis that includes Planck bispectrum data. The new Planck polarization data provide a stringent test of the adiabaticity of the initial conditions. The polarization data also provide improved constraints on inflationary models that predict a small statistically anisotropic quadrupolar modulation of the primordial fluctuations. However, the polarization data do not confirm physical models for a scale-dependent dipolar modulation. ## Authors Planck Collaboration, Y. Akrami, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, J. Carron, A. Challinor, H. C. Chiang, L. P. L. Colombo, C. Combet, D. Contreras, B. P. Crill, F. Cuttaia, P. de Bernardis, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, J. M. Diego, S. Donzelli, O. Doré, M. Douspis, A. Ducout, X. Dupac, S. Dusini, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, J. Fergusson, R. Fernandez-Cobos, F. Finelli, F. Forastieri, M. Frailis, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, C. Gauthier, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, D. C. Hooper, Z. Huang, A. H. Jaffe, W. C. Jones, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, V. Lindholm, M. Lpez-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. D. Meerburg, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, S. Mitra, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, M. Münchmeyer, P. Natoli, H. U. Nørgaard-Nielsen, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, H. V. Peiris, F. Perrotta, V. Pettorino, F. Piacentini, L. Polastri, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, E. P. S. Shellard, M. Shiraishi, C. Sirignano, G. Sirri, L. D. Spencer, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, S. D. M. White, A. Zacchei, J. P. Zibin, A. Zonca ## Published 2018-07-17T04:05:09Z # Planck 2018 results. VIII. Gravitational lensing [1807.06210](entry.id) ## Abstract We present measurements of the cosmic microwave background (CMB) lensing potential using the final $\textit{Planck}$ 2018 temperature and polarization data. We increase the significance of the detection of lensing in the polarization maps from $5\,\sigma$ to $9\,\sigma$. Combined with temperature, lensing is detected at $40\,\sigma$. We present an extensive set of tests of the robustness of the lensing-potential power spectrum, and construct a minimum-variance estimator likelihood over lensing multipoles $8 \le L \le 400$. We find good consistency between lensing constraints and the results from the $\textit{Planck}$ CMB power spectra within the $\rm{\Lambda CDM}$ model. Combined with baryon density and other weak priors, the lensing analysis alone constrains $\sigma_8 \Omega_{\rm m}^{0.25}=0.589\pm 0.020$ ($1\,\sigma$ errors). Also combining with baryon acoustic oscillation (BAO) data, we find tight individual parameter constraints, $\sigma_8=0.811\pm0.019$, $H_0=67.9_{-1.3}^{+1.2}\,\text{km}\,\text{s}^{-1}\,\rm{Mpc}^{-1}$, and $\Omega_{\rm m}=0.303^{+0.016}_{-0.018}$. Combining with $\textit{Planck}$ CMB power spectrum data, we measure $\sigma_8$ to better than $1\,\%$ precision, finding $\sigma_8=0.811\pm 0.006$. We find consistency with the lensing results from the Dark Energy Survey, and give combined lensing-only parameter constraints that are tighter than joint results using galaxy clustering. Using $\textit{Planck}$ cosmic infrared background (CIB) maps we make a combined estimate of the lensing potential over $60\,\%$ of the sky with considerably more small-scale signal. We demonstrate delensing of the $\textit{Planck}$ power spectra, detecting a maximum removal of $40\,\%$ of the lensing-induced power in all spectra. The improvement in the sharpening of the acoustic peaks by including both CIB and the quadratic lensing reconstruction is detected at high significance (abridged). ## Authors Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, E. Calabrese, J. -F. Cardoso, J. Carron, A. Challinor, H. C. Chiang, L. P. L. Colombo, C. Combet, B. P. Crill, F. Cuttaia, P. de Bernardis, G. de Zotti, J. Delabrouille, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, R. Fernandez-Cobos, F. Forastieri, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, L. Knox, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, A. Melchiorri, A. Mennella, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, P. Natoli, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, F. Perrotta, V. Pettorino, F. Piacentini, L. Polastri, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, C. Sirignano, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, M. White, S. D. M. White, A. Zacchei, A. Zonca ## Published 2018-07-17T04:05:08Z # Logolinear series expansions with applications to primordial cosmology [1901.07540](entry.id) ## Abstract We develop a method for computing series expansions for solutions to ordinary differential equations when the asymptotic form contains both linear and logarithmic terms. Such situations are common in primordial cosmology when considering series expansions out of a singularity in the equations arising from a pre-inflationary phase of the universe. We develop mathematical techniques for generating these series expansions, and apply them to polynomial and Starobinsky inflationary potentials with kinetic initial conditions. Code for analytic and numerical computation of logolinear series is provided on GitHub. ## Authors Will Handley, Anthony Lasenby, Mike Hobson ## Published 2019-01-21T20:24:07Z # Planck 2018 results. IX. Constraints on primordial non-Gaussianity [1905.05697](entry.id) ## Abstract We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following results: f_NL^local = -0.9 +\- 5.1; f_NL^equil = -26 +\- 47; and f_NL^ortho = - 38 +\- 24 (68%CL, statistical). These results include the low-multipole (4 <= l < 40) polarization data, not included in our previous analysis, pass an extensive battery of tests, and are stable with respect to our 2015 measurements. Polarization bispectra display a significant improvement in robustness; they can now be used independently to set NG constraints. We consider a large number of additional cases, e.g. scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 sigma. We present model-independent reconstructions and analyses of the CMB bispectrum. Our final constraint on the local trispectrum shape is g_NLl^local = (-5.8 +\-6.5) x 10^4 (68%CL, statistical), while constraints for other trispectra are also determined. We constrain the parameter space of different early-Universe scenarios, including general single-field models of inflation, multi-field and axion field parity-breaking models. Our results provide a high-precision test for structure-formation scenarios, in complete agreement with the basic picture of the LambdaCDM cosmology regarding the statistics of the initial conditions (abridged). ## Authors Planck Collaboration, Y. Akrami, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, F. R. Bouchet, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, B. Casaponsa, A. Challinor, H. C. Chiang, L. P. L. Colombo, C. Combet, B. P. Crill, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, S. Dusini, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, J. Fergusson, R. Fernandez-Cobos, F. Finelli, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, K. Ganga, R. T. Génova-Santos, M. Gerbino, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, G. Jung, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. D. Meerburg, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, M. Münchmeyer, P. Natoli, F. Oppizzi, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, F. Perrotta, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, B. Racine, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Savelainen, D. Scott, E. P. S. Shellard, M. Shiraishi, C. Sirignano, G. Sirri, K. Smith, L. D. Spencer, L. Stanco, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2019-05-14T16:19:37Z # anesthetic: nested sampling visualisation [1905.04768](entry.id) ## Abstract anesthetic is a Python package for processing nested sampling runs, and will be useful for any scientist or statistician who uses nested sampling software. anesthetic unifies many existing tools and techniques in an extensible framework that is intuitive for users familiar with the standard Python packages, namely NumPy, SciPy, Matplotlib and pandas. ## Authors Will Handley ## Published 2019-05-12T18:37:10Z # Maximum-Entropy Priors with Derived Parameters in a Specified Distribution [1804.08143](entry.id) ## Abstract We propose a method for transforming probability distributions so that parameters of interest are forced into a specified distribution. We prove that this approach is the maximum entropy choice, and provide a motivating example applicable to neutrino hierarchy inference. ## Authors Will Handley, Marius Millea ## Published 2018-04-22T17:39:04Z # Planck 2018 results. XII. Galactic astrophysics using polarized dust emission [1807.06212](entry.id) ## Abstract We present 353 GHz full-sky maps of the polarization fraction $p$, angle $\psi$, and dispersion of angles $S$ of Galactic dust thermal emission produced from the 2018 release of Planck data. We confirm that the mean and maximum of $p$ decrease with increasing $N_H$. The uncertainty on the maximum polarization fraction, $p_\mathrm{max}=22.0$% at 80 arcmin resolution, is dominated by the uncertainty on the zero level in total intensity. The observed inverse behaviour between $p$ and $S$ is interpreted with models of the polarized sky that include effects from only the topology of the turbulent Galactic magnetic field. Thus, the statistical properties of $p$, $\psi$, and $S$ mostly reflect the structure of the magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map $S \times p$, looking for residual trends. While $p$ decreases by a factor of 3--4 between $N_H=10^{20}$ cm$^{-2}$ and $N_H=2\times 10^{22}$ cm$^{-2}$, $S \times p$ decreases by only about 25%, a systematic trend observed in both the diffuse ISM and molecular clouds. Second, we find no systematic trend of $S \times p$ with the dust temperature, even though in the diffuse ISM lines of sight with high $p$ and low $S$ tend to have colder dust. We also compare Planck data with starlight polarization in the visible at high latitudes. The agreement in polarization angles is remarkable. Two polarization emission-to-extinction ratios that characterize dust optical properties depend only weakly on $N_H$ and converge towards the values previously determined for translucent lines of sight. We determine an upper limit for the polarization fraction in extinction of 13%, compatible with the $p_\mathrm{max}$ observed in emission. These results provide strong constraints for models of Galactic dust in diffuse gas. ## Authors Planck Collaboration, N. Aghanim, Y. Akrami, M. I. R. Alves, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, A. Bracco, M. Bucher, C. Burigana, E. Calabrese, J. -F. Cardoso, J. Carron, R. -R. Chary, H. C. Chiang, L. P. L. Colombo, C. Combet, B. P. Crill, F. Cuttaia, P. de Bernardis, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, C. Dickinson, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, E. Falgarone, Y. Fantaye, R. Fernandez-Cobos, K. Ferrière, F. Finelli, F. Forastieri, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, G. Green, A. Gruppuso, J. E. Gudmundsson, V. Guillet, W. Handley, F. K. Hansen, G. Helou, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, A. Marcos-Caballero, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, A. Melchiorri, A. Mennella, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, P. Natoli, L. Pagano, D. Paoletti, G. Patanchon, F. Perrotta, V. Pettorino, F. Piacentini, L. Polastri, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, I. Ristorcelli, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, C. Sirignano, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, F. Vansyngel, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2018-07-17T04:05:10Z # The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up [1811.11679](entry.id) ## Abstract Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the last decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this article we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semi-stochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included. ## Authors James S. Spencer, Nick S. Blunt, Seonghoon Choi, Jiri Etrych, Maria-Andreea Filip, W. M. C. Foulkes, Ruth S. T. Franklin, Will J. Handley, Fionn D. Malone, Verena A. Neufeld, Roberto Di Remigio, Thomas W. Rogers, Charles J. C. Scott, James J. Shepherd, William A. Vigor, Joseph Weston, RuQing Xu, Alex J. W. Thom ## Published 2018-11-28T17:01:36Z # Bayesian sparse reconstruction: a brute-force approach to astronomical imaging and machine learning [1809.04598](entry.id) ## Abstract We present a principled Bayesian framework for signal reconstruction, in which the signal is modelled by basis functions whose number (and form, if required) is determined by the data themselves. This approach is based on a Bayesian interpretation of conventional sparse reconstruction and regularisation techniques, in which sparsity is imposed through priors via Bayesian model selection. We demonstrate our method for noisy 1- and 2-dimensional signals, including astronomical images. Furthermore, by using a product-space approach, the number and type of basis functions can be treated as integer parameters and their posterior distributions sampled directly. We show that order-of-magnitude increases in computational efficiency are possible from this technique compared to calculating the Bayesian evidences separately, and that further computational gains are possible using it in combination with dynamic nested sampling. Our approach can also be readily applied to neural networks, where it allows the network architecture to be determined by the data in a principled Bayesian manner by treating the number of nodes and hidden layers as parameters. ## Authors Edward Higson, Will Handley, Michael Hobson, Anthony Lasenby ## Published 2018-09-12T18:00:01Z # Planck 2018 results. XI. Polarized dust foregrounds [1801.04945](entry.id) ## Abstract The study of polarized dust emission has become entwined with the analysis of the cosmic microwave background (CMB) polarization. We use new Planck maps to characterize Galactic dust emission as a foreground to the CMB polarization. We present Planck EE, BB, and TE power spectra of dust polarization at 353 GHz for six nested sky regions covering from 24 to 71 % of the sky. We present power-law fits to the angular power spectra, yielding evidence for statistically significant variations of the exponents over sky regions and a difference between the values for the EE and BB spectra. The TE correlation and E/B power asymmetry extend to low multipoles that were not included in earlier Planck polarization papers. We also report evidence for a positive TB dust signal. Combining data from Planck and WMAP, we determine the amplitudes and spectral energy distributions (SEDs) of polarized foregrounds, including the correlation between dust and synchrotron polarized emission, for the six sky regions as a function of multipole. This quantifies the challenge of the component separation procedure required for detecting the reionization and recombination peaks of primordial CMB B modes. The SED of polarized dust emission is fit well by a single-temperature modified blackbody emission law from 353 GHz to below 70 GHz. For a dust temperature of 19.6 K, the mean spectral index for dust polarization is $\beta_{\rm d}^{P} = 1.53\pm0.02 $. By fitting multi-frequency cross-spectra, we examine the correlation of the dust polarization maps across frequency. We find no evidence for decorrelation. If the Planck limit for the largest sky region applies to the smaller sky regions observed by sub-orbital experiments, then decorrelation might not be a problem for CMB experiments aiming at a primordial B-mode detection limit on the tensor-to-scalar ratio $r\simeq0.01$ at the recombination peak. ## Authors Planck Collaboration, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, A. Bracco, M. Bucher, C. Burigana, E. Calabrese, J. -F. Cardoso, J. Carron, H. C. Chiang, C. Combet, B. P. Crill, P. de Bernardis, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, C. Dickinson, J. M. Diego, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, E. Falgarone, Y. Fantaye, K. Ferrière, F. Finelli, F. Forastieri, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, T. Ghosh, J. González-Nuevo, K. M. Górski, A. Gruppuso, J. E. Gudmundsson, V. Guillet, W. Handley, F. K. Hansen, D. Herranz, Z. Huang, A. H. Jaffe, W. C. Jones, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, J. -M. Lamarre, A. Lasenby, M. Le Jeune, F. Levrier, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, P. G. Martin, E. Martínez-González, S. Matarrese, J. D. McEwen, P. R. Meinhold, A. Melchiorri, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, P. Natoli, L. Pagano, D. Paoletti, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, C. Rosset, G. Roudier, J. A. Rubiño-Martín, B. Ruiz-Granados, L. Salvati, M. Sandri, M. Savelainen, D. Scott, J. D. Soler, L. D. Spencer, J. A. Tauber, D. Tavagnacco, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, F. Vansyngel, F. Van Tent, P. Vielva, F. Villa, N. Vittorio, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2018-01-15T19:00:44Z # Dynamic nested sampling: an improved algorithm for parameter estimation and evidence calculation [1704.03459](entry.id) ## Abstract We introduce dynamic nested sampling: a generalisation of the nested sampling algorithm in which the number of "live points" varies to allocate samples more efficiently. In empirical tests the new method significantly improves calculation accuracy compared to standard nested sampling with the same number of samples; this increase in accuracy is equivalent to speeding up the computation by factors of up to ~72 for parameter estimation and ~7 for evidence calculations. We also show that the accuracy of both parameter estimation and evidence calculations can be improved simultaneously. In addition, unlike in standard nested sampling, more accurate results can be obtained by continuing the calculation for longer. Popular standard nested sampling implementations can be easily adapted to perform dynamic nested sampling, and several dynamic nested sampling software packages are now publicly available. ## Authors Edward Higson, Will Handley, Mike Hobson, Anthony Lasenby ## Published 2017-04-11T18:00:00Z # nestcheck: diagnostic tests for nested sampling calculations [1804.06406](entry.id) ## Abstract Nested sampling is an increasingly popular technique for Bayesian computation, in particular for multimodal, degenerate problems of moderate to high dimensionality. Without appropriate settings, however, nested sampling software may fail to explore such posteriors correctly; for example producing correlated samples or missing important modes. This paper introduces new diagnostic tests to assess the reliability both of parameter estimation and evidence calculations using nested sampling software, and demonstrates them empirically. We present two new diagnostic plots for nested sampling, and give practical advice for nested sampling software users in astronomy and beyond. Our diagnostic tests and diagrams are implemented in nestcheck: a publicly available Python package for analysing nested sampling calculations, which is compatible with output from MultiNest, PolyChord and dyPolyChord. ## Authors Edward Higson, Will Handley, Mike Hobson, Anthony Lasenby ## Published 2018-04-16T18:00:02Z # Constraining the kinetically dominated Universe [1809.07737](entry.id) ## Abstract We present cosmological constraints from Planck 2015 data for a universe that is kinetically dominated at very early times. We perform a Markov chain Monte Carlo analysis to estimate parameters and use nested sampling to determine the evidence for a model comparison of the single-field quadratic and Starobinsky inflationary models with the standard $\Lambda$CDM cosmology. In particular we investigate how different amounts of inflation before and after horizon exit affect the primordial power spectrum and subsequently the power spectrum of the cosmic microwave background. We find that the model using kinetically dominated initial conditions for inflation performs similarly well in terms of Bayesian evidence as a model directly starting out in the slow-roll phase, despite having an additional parameter. The data show a slight preference for a cutoff at large scales in the primordial and temperature power spectra. ## Authors L. T. Hergt, W. J. Handley, M. P. Hobson, A. N. Lasenby ## Published 2018-09-20T16:57:22Z # A case for kinetically dominated initial conditions for inflation [1809.07185](entry.id) ## Abstract We make a case for setting initial conditions for inflation at the Planck epoch in the kinetically dominated regime. For inflationary potentials with a plateau or a hill, i.e. potentials that are bounded from above within a certain region of interest, we cannot claim complete ignorance of the energy distribution between kinetic and potential energy, and equipartition of energy at the Planck epoch becomes questionable. We analyse different classes of potentials in phase-space and quantify the fraction of the Planck surface that is kinetically dominated. For the small amplitudes of the potentials as suggested by current data, the Planck surface lies in the region of kinetic dominance for almost all values of interest of the inflaton field. ## Authors L. T. Hergt, W. J. Handley, M. P. Hobson, A. N. Lasenby ## Published 2018-09-19T13:41:10Z # Kinetic Initial Conditions for Inflation [1401.2253](entry.id) ## Abstract We consider the classical evolution of the inflaton field $\phi(t)$ and the Hubble parameter $H(t)$ in homogeneous and isotropic single-field inflation models. Under an extremely broad assumption, we show that the universe generically emerges from an initial singularity in a non-inflating state where the kinetic energy of the inflaton dominates its potential energy, $\dot{\phi}^2 \gg V(\phi)$. In this kinetically-dominated regime, the dynamical equations admit simple analytic solutions for $\phi(t)$ and $H(t)$, which are independent of the form of $V(\phi)$. In such models, these analytic solutions thus provide a simple way of setting the initial conditions from which to start the (usually numerical) integration of the coupled equations of motion for $\phi(t)$ and $H(t)$. We illustrate this procedure by applying it to spatially-flat models with polynomial and exponential potentials, and determine the background evolution in each case; generically $H(t)$ and $|\phi(t)|$ as well as their time derivatives decrease during kinetic dominance until $\dot{\phi}^2\sim V(\phi)$, marking the onset of a brief period of fast-roll inflation prior to a slow roll phase. We also calculate the approximate spectrum of scalar perturbations produced in each model and show that it exhibits a generic damping of power on large scales. This may be relevant to the apparent low-$\ell$ falloff in the CMB power spectrum. ## Authors W. J. Handley, S. D. Brechet, A. N. Lasenby, M. P. Hobson ## Published 2014-01-10T08:34:23Z # Planck intermediate results. LIV. The Planck Multi-frequency Catalogue of Non-thermal Sources [1802.08649](entry.id) ## Abstract This paper presents the Planck Multi-frequency Catalogue of Non-thermal (i.e. synchrotron-dominated) Sources (PCNT) observed between 30 and 857 GHz by the ESA Planck mission. This catalogue was constructed by selecting objects detected in the full mission all-sky temperature maps at 30 and 143 GHz, with a signal-to-noise ratio (S/N)>3 in at least one of the two channels after filtering with a particular Mexican hat wavelet. As a result, 29400 source candidates were selected. Then, a multi-frequency analysis was performed using the Matrix Filters methodology at the position of these objects, and flux densities and errors were calculated for all of them in the nine Planck channels. The present catalogue is the first unbiased, full-sky catalogue of synchrotron-dominated sources published at millimetre and submillimetre wavelengths and constitutes a powerful database for statistical studies of non-thermal extragalactic sources, whose emission is dominated by the central active galactic nucleus. Together with the full multi-frequency catalogue, we also define the Bright Planck Multi-frequency Catalogue of Non-thermal Sources PCNTb, where only those objects with a S/N>4 at both 30 and 143 GHz were selected. In this catalogue 1146 compact sources are detected outside the adopted Planck GAL070 mask; thus, these sources constitute a highly reliable sample of extragalactic radio sources. We also flag the high-significance subsample PCNThs, a subset of 151 sources that are detected with S/N>4 in all nine Planck channels, 75 of which are found outside the Planck mask adopted here. The remaining 76 sources inside the Galactic mask are very likely Galactic objects. ## Authors Planck Collaboration, Y. Akrami, F. Argüeso, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, L. Bonavera, J. R. Bond, J. Borrill, F. R. Bouchet, C. Burigana, R. C. Butler, E. Calabrese, J. Carron, H. C. Chiang, C. Combet, B. P. Crill, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, C. Dickinson, J. M. Diego, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, F. Finelli, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, A. Lähteenmäki, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, F. Levrier, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, J. D. McEwen, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, P. Natoli, C. A. Oxborrow, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, T. J. Pearson, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, B. Racine, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, G. Roudier, J. A. Rubiño-Martín, L. Salvati, M. Sandri, M. Savelainen, D. Scott, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, L. Toffolatti, M. Tomasi, T. Trombetti, M. Tucci, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2018-02-23T17:27:56Z # Planck 2018 results. II. Low Frequency Instrument data processing [1807.06206](entry.id) ## Abstract We present a final description of the data-processing pipeline for the Planck, Low Frequency Instrument (LFI), implemented for the 2018 data release. Several improvements have been made with respect to the previous release, especially in the calibration process and in the correction of instrumental features such as the effects of nonlinearity in the response of the analogue-to-digital converters. We provide a brief pedagogical introduction to the complete pipeline, as well as a detailed description of the important changes implemented. Self-consistency of the pipeline is demonstrated using dedicated simulations and null tests. We present the final version of the LFI full sky maps at 30, 44, and 70 GHz, both in temperature and polarization, together with a refined estimate of the Solar dipole and a final assessment of the main LFI instrumental parameters. ## Authors Planck Collaboration, Y. Akrami, F. Argüeso, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, L. Bonavera, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, L. P. L. Colombo, B. P. Crill, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, E. Di Valentino, C. Dickinson, J. M. Diego, S. Donzelli, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, Y. Fantaye, F. Finelli, M. Frailis, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, J. P. Leahy, F. Levrier, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, M. Maris, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, P. R. Meinhold, A. Melchiorri, A. Mennella, M. Migliaccio, D. Molinari, L. Montier, G. Morgante, A. Moss, P. Natoli, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, L. Patrizii, M. Peel, F. Perrotta, V. Pettorino, F. Piacentini, G. Polenta, J. -L. Puget, J. P. Rachen, B. Racine, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, G. Roudier, J. A. Rubiño-Martín, L. Salvati, M. Sandri, M. Savelainen, D. Scott, D. S. Seljebotn, C. Sirignano, G. Sirri, L. D. Spencer, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Terenzi, L. Toffolatti, M. Tomasi, T. Trombetti, J. Valiviita, F. Vansyngel, B. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, R. Watson, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2018-07-17T04:05:04Z # Planck intermediate results. LIII. Detection of velocity dispersion from the kinetic Sunyaev-Zeldovich effect [1707.00132](entry.id) ## Abstract Using the ${\it Planck}$ full-mission data, we present a detection of the temperature (and therefore velocity) dispersion due to the kinetic Sunyaev-Zeldovich (kSZ) effect from clusters of galaxies. To suppress the primary CMB and instrumental noise we derive a matched filter and then convolve it with the ${\it Planck}$ foreground-cleaned `${\tt 2D-ILC\,}$' maps. By using the Meta Catalogue of X-ray detected Clusters of galaxies (MCXC), we determine the normalized ${\it rms}$ dispersion of the temperature fluctuations at the positions of clusters, finding that this shows excess variance compared with the noise expectation. We then build an unbiased statistical estimator of the signal, determining that the normalized mean temperature dispersion of $1526$ clusters is $\langle \left(\Delta T/T \right)^{2} \rangle = (1.64 \pm 0.48) \times 10^{-11}$. However, comparison with analytic calculations and simulations suggest that around $0.7\,\sigma$ of this result is due to cluster lensing rather than the kSZ effect. By correcting this, the temperature dispersion is measured to be $\langle \left(\Delta T/T \right)^{2} \rangle = (1.35 \pm 0.48) \times 10^{-11}$, which gives a detection at the $2.8\,\sigma$ level. We further convert uniform-weight temperature dispersion into a measurement of the line-of-sight velocity dispersion, by using estimates of the optical depth of each cluster (which introduces additional uncertainty into the estimate). We find that the velocity dispersion is $\langle v^{2} \rangle =(123\,000 \pm 71\,000)\,({\rm km}\,{\rm s}^{-1})^{2}$, which is consistent with findings from other large-scale structure studies, and provides direct evidence of statistical homogeneity on scales of $600\,h^{-1}{\rm Mpc}$. Our study shows the promise of using cross-correlations of the kSZ effect with large-scale structure in order to constrain the growth of structure. ## Authors Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, R. Battye, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, F. R. Bouchet, C. Burigana, E. Calabrese, J. Carron, H. C. Chiang, B. Comis, D. Contreras, B. P. Crill, A. Curto, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, E. Di Valentino, C. Dickinson, J. M. Diego, O. Doré, A. Ducout, X. Dupac, F. Elsner, T. A. Enßlin, H. K. Eriksen, E. Falgarone, Y. Fantaye, F. Finelli, F. Forastieri, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, M. Gerbino, K. M. Górski, A. Gruppuso, J. E. Gudmundsson, W. Handley, F. K. Hansen, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, F. Levrier, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, A. Melchiorri, A. Mennella, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, P. Natoli, C. A. Oxborrow, L. Pagano, D. Paoletti, B. Partridge, O. Perdereau, L. Perotto, V. Pettorino, F. Piacentini, S. Plaszczynski, L. Polastri, G. Polenta, J. P. Rachen, B. Racine, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, G. Roudier, B. Ruiz-Granados, M. Sandri, M. Savelainen, D. Scott, C. Sirignano, G. Sirri, L. D. Spencer, L. Stanco, R. Sunyaev, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, M. Tristram, T. Trombetti, J. Valiviita, F. Van Tent, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, A. Zacchei, A. Zonca ## Published 2017-07-01T10:03:56Z # Planck 2018 results. III. High Frequency Instrument data processing and frequency maps [1807.06207](entry.id) ## Abstract This paper presents the High Frequency Instrument (HFI) data processing procedures for the Planck 2018 release. Major improvements in mapmaking have been achieved since the previous 2015 release. They enabled the first significant measurement of the reionization optical depth parameter using HFI data. This paper presents an extensive analysis of systematic effects, including the use of simulations to facilitate their removal and characterize the residuals. The polarized data, which presented a number of known problems in the 2015 Planck release, are very significantly improved. Calibration, based on the CMB dipole, is now extremely accurate and in the frequency range 100 to 353 GHz reduces intensity-to-polarization leakage caused by calibration mismatch. The Solar dipole direction has been determined in the three lowest HFI frequency channels to within one arc minute, and its amplitude has an absolute uncertainty smaller than $0.35\mu$K, an accuracy of order $10^{-4}$. This is a major legacy from the HFI for future CMB experiments. The removal of bandpass leakage has been improved by extracting the bandpass-mismatch coefficients for each detector as part of the mapmaking process; these values in turn improve the intensity maps. This is a major change in the philosophy of "frequency maps", which are now computed from single detector data, all adjusted to the same average bandpass response for the main foregrounds. Simulations reproduce very well the relative gain calibration of detectors, as well as drifts within a frequency induced by the residuals of the main systematic effect. Using these simulations, we measure and correct the small frequency calibration bias induced by this systematic effect at the $10^{-4}$ level. There is no detectable sign of a residual calibration bias between the first and second acoustic peaks in the CMB channels, at the $10^{-3}$ level. ## Authors Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, S. Basak, K. Benabed, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, E. Calabrese, J. -F. Cardoso, J. Carron, A. Challinor, H. C. Chiang, L. P. L. Colombo, C. Combet, F. Couchot, B. P. Crill, F. Cuttaia, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, J. -M. Delouis, E. Di Valentino, J. M. Diego, O. Doré, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Enßlin, H. K. Eriksen, E. Falgarone, Y. Fantaye, F. Finelli, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frolov, S. Galeotta, S. Galli, K. Ganga, R. T. Génova-Santos, M. Gerbino, T. Ghosh, J. González-Nuevo, K. M. Górski, S. Gratton, A. Gruppuso, J. E. Gudmundsson, W. Handley, F. K. Hansen, S. Henrot-Versillé, D. Herranz, E. Hivon, Z. Huang, A. H. Jaffe, W. C. Jones, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, G. Lagache, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, F. Levrier, M. Liguori, P. B. Lilje, V. Lindholm, M. López-Caniego, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, P. G. Martin, E. Martínez-González, S. Matarrese, N. Mauri, J. D. McEwen, A. Melchiorri, A. Mennella, M. Migliaccio, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, G. Morgante, A. Moss, S. Mottet, P. Natoli, L. Pagano, D. Paoletti, B. Partridge, G. Patanchon, L. Patrizii, O. Perdereau, F. Perrotta, V. Pettorino, F. Piacentini, J. -L. Puget, J. P. Rachen, M. Reinecke, M. Remazeilles, A. Renzi, G. Rocha, G. Roudier, L. Salvati, M. Sandri, M. Savelainen, D. Scott, C. Sirignano, G. Sirri, L. D. Spencer, R. Sunyaev, A. -S. Suur-Uski, J. A. Tauber, D. Tavagnacco, M. Tenti, L. Toffolatti, M. Tomasi, M. Tristram, T. Trombetti, J. Valiviita, F. Vansyngel, B. Van Tent, L. Vibert, P. Vielva, F. Villa, N. Vittorio, B. D. Wandelt, I. K. Wehus, A. Zonca ## Published 2018-07-17T04:05:05Z # On the Feasibility of Intense Radial Velocity Surveys for Earth-twin Discoveries [1806.00518](entry.id) ## Abstract This work assesses the potential capability of the next generation of high-precision Radial Velocity (RV) instruments for Earth-twin exoplanet detection. From the perspective of the importance of data sampling, the Terra Hunting Experiment aims to do this through an intense series of nightly RV observations over a long baseline on a carefully selected target list, via the brand-new instrument HARPS3. This paper describes an end-to-end simulation of generating and processing such data to help us better understand the impact of uncharacterised stellar noise in the recovery of Earth-mass planets with orbital periods of the order of many months. We consider full Keplerian systems, realistic simulated stellar noise, instrument white noise, and location-specific weather patterns for our observation schedules. We use Bayesian statistics to assess various planetary models fitted to the synthetic data, and compare the successful planet recovery of the Terra Hunting Experiment schedule with a typical reference survey. We find that the Terra Hunting Experiment can detect Earth-twins in the habitable zones of solar-type stars, in single and multi-planet systems, and in the presence of stellar signals. Also that it out-performs a typical reference survey on accuracy of recovered parameters, and that it performs comparably to an uninterrupted space-based schedule. ## Authors Richard D. Hall, Samantha J. Thompson, Will Handley, Didier Queloz ## Published 2018-06-01T19:33:56Z # Towards a framework for testing general relativity with extreme-mass-ratio-inspiral observations [1803.10210](entry.id) ## Abstract Extreme-mass-ratio-inspiral observations from future space-based gravitational-wave detectors such as LISA will enable strong-field tests of general relativity with unprecedented precision, but at prohibitive computational cost if existing statistical techniques are used. In one such test that is currently employed for LIGO black-hole binary mergers, generic deviations from relativity are represented by $N$ deformation parameters in a generalised waveform model; the Bayesian evidence for each of its $2^N$ combinatorial submodels is then combined into a posterior odds ratio for modified gravity over relativity in a null-hypothesis test. We adapt and apply this test to a generalised model for extreme-mass-ratio inspirals constructed on deformed black-hole spacetimes, and focus our investigation on how computational efficiency can be increased through an evidence-free method of model selection. This method is akin to the algorithm known as product-space Markov chain Monte Carlo, but uses nested sampling and improved error estimates from a rethreading technique. We perform benchmarking and robustness checks for the method, and find order-of-magnitude computational gains over regular nested sampling in the case of synthetic data generated from the null model. ## Authors Alvin J. K. Chua, Sonke Hee, Will J. Handley, Edward Higson, Christopher J. Moore, Jonathan R. Gair, Michael P. Hobson, Anthony N. Lasenby ## Published 2018-03-27T17:49:29Z # Sampling Errors in Nested Sampling Parameter Estimation [1703.09701](entry.id) ## Abstract Sampling errors in nested sampling parameter estimation differ from those in Bayesian evidence calculation, but have been little studied in the literature. This paper provides the first explanation of the two main sources of sampling errors in nested sampling parameter estimation, and presents a new diagrammatic representation for the process. We find no current method can accurately measure the parameter estimation errors of a single nested sampling run, and propose a method for doing so using a new algorithm for dividing nested sampling runs. We empirically verify our conclusions and the accuracy of our new method. ## Authors Edward Higson, Will Handley, Mike Hobson, Anthony Lasenby ## Published 2017-03-28T18:00:00Z # Planck 2015 results. XX. Constraints on inflation [1502.02114](entry.id) ## Abstract We present the implications for cosmic inflation of the Planck measurements of the cosmic microwave background (CMB) anisotropies in both temperature and polarization based on the full Planck survey. The Planck full mission temperature data and a first release of polarization data on large angular scales measure the spectral index of curvature perturbations to be $n_\mathrm{s} = 0.968 \pm 0.006$ and tightly constrain its scale dependence to $d n_s/d \ln k =-0.003 \pm 0.007$ when combined with the Planck lensing likelihood. When the high-$\ell$ polarization data is included, the results are consistent and uncertainties are reduced. The upper bound on the tensor-to-scalar ratio is $r_{0.002} < 0.11$ (95% CL), consistent with the B-mode polarization constraint $r< 0.12$ (95% CL) obtained from a joint BICEP2/Keck Array and Planck analysis. These results imply that $V(\phi) \propto \phi^2$ and natural inflation are now disfavoured compared to models predicting a smaller tensor-to-scalar ratio, such as $R^2$ inflation. Three independent methods reconstructing the primordial power spectrum are investigated. The Planck data are consistent with adiabatic primordial perturbations. We investigate inflationary models producing an anisotropic modulation of the primordial curvature power spectrum as well as generalized models of inflation not governed by a scalar field with a canonical kinetic term. The 2015 results are consistent with the 2013 analysis based on the nominal mission data. ## Authors Planck Collaboration, P. A. R. Ade, N. Aghanim, M. Arnaud, F. Arroja, M. Ashdown, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, N. Bartolo, E. Battaner, K. Benabed, A. Benoit, A. Benoit-Levy, J. -P. Bernard, M. Bersanelli, P. Bielewicz, J. J. Bock, A. Bonaldi, L. Bonavera, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, A. Catalano, A. Challinor, A. Chamballu, R. -R. Chary, H. C. Chiang, P. R. Christensen, S. Church, D. L. Clements, S. Colombi, L. P. L. Colombo, C. Combet, D. Contreras, F. Couchot, A. Coulais, B. P. Crill, A. Curto, F. Cuttaia, L. Danese, R. D. Davies, R. J. Davis, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, F. -X. Desert, J. M. Diego, H. Dole, S. Donzelli, O. Dore, M. Douspis, A. Ducout, X. Dupac, G. Efstathiou, F. Elsner, T. A. Ensslin, H. K. Eriksen, J. Fergusson, F. Finelli, O. Forni, M. Frailis, A. A. Fraisse, E. Franceschi, A. Frejsel, A. Frolov, S. Galeotta, S. Galli, K. Ganga, C. Gauthier, M. Giard, Y. Giraud-Heraud, E. Gjerlow, J. Gonzalez-Nuevo, K. M. Gorski, S. Gratton, A. Gregorio, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Hanson, D. L. Harrison, S. Henrot-Versille, C. Hernandez-Monteagudo, D. Herranz, S. R. Hildebrandt, E. Hivon, M. Hobson, W. A. Holmes, A. Hornstrup, W. Hovest, Z. Huang, K. M. Huffenberger, G. Hurier, A. H. Jaffe, T. R. Jaffe, W. C. Jones, M. Juvela, E. Keihanen, R. Keskitalo, J. Kim, T. S. Kisner, R. Kneissl, J. Knoche, M. Kunz, H. Kurki-Suonio, G. Lagache, A. Lahteenmaki, J. -M. Lamarre, A. Lasenby, M. Lattanzi, C. R. Lawrence, R. Leonardi, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Linden-Vornle, M. Lopez-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macias-Perez, G. Maggio, D. Maino, N. Mandolesi, A. Mangilli, M. Maris, P. G. Martin, E. Martinez-Gonzalez, S. Masi, S. Matarrese, P. McGehee, P. R. Meinhold, A. Melchiorri, L. Mendes, A. Mennella, M. Migliaccio, S. Mitra, M. -A. Miville-Deschenes, D. Molinari, A. Moneti, L. Montier, G. Morgante, D. Mortlock, A. Moss, M. Munchmeyer, D. Munshi, J. A. Murphy, P. Naselsky, F. Nati, P. Natoli, C. B. Netterfield, H. U. Norgaard-Nielsen, F. Noviello, D. Novikov, I. Novikov, C. A. Oxborrow, F. Paci, L. Pagano, F. Pajot, R. Paladini, S. Pandolfi, D. Paoletti, F. Pasian, G. Patanchon, T. J. Pearson, H. V. Peiris, O. Perdereau, L. Perotto, F. Perrotta, V. Pettorino, F. Piacentini, M. Piat, E. Pierpaoli, D. Pietrobon, S. Plaszczynski, E. Pointecouteau, G. Polenta, L. Popa, G. W. Pratt, G. Prezeau, S. Prunet, J. -L. Puget, J. P. Rachen, W. T. Reach, R. Rebolo, M. Reinecke, M. Remazeilles, C. Renault, A. Renzi, I. Ristorcelli, G. Rocha, C. Rosset, M. Rossetti, G. Roudier, M. Rowan-Robinson, J. A. Rubino-Martin, B. Rusholme, M. Sandri, D. Santos, M. Savelainen, G. Savini, D. Scott, M. D. Seiffert, E. P. S. Shellard, M. Shiraishi, L. D. Spencer, V. Stolyarov, R. Stompor, R. Sudiwala, R. Sunyaev, D. Sutton, A. -S. Suur-Uski, J. -F. Sygnet, J. A. Tauber, L. Terenzi, L. Toffolatti, M. Tomasi, M. Tristram, T. Trombetti, M. Tucci, J. Tuovinen, L. Valenziano, J. Valiviita, B. Van Tent, P. Vielva, F. Villa, L. A. Wade, B. D. Wandelt, I. K. Wehus, M. White, D. Yvon, A. Zacchei, J. P. Zibin, A. Zonca ## Published 2015-02-07T09:08:50Z # Exploring cosmic origins with CORE: effects of observer peculiar motion [1704.05764](entry.id) ## Abstract We discuss the effects on the CMB, CIB, and thermal SZ effect due to the peculiar motion of an observer with respect to the CMB rest frame, which induces boosting effects. We investigate the scientific perspectives opened by future CMB space missions, focussing on the CORE proposal. The improvements in sensitivity offered by a mission like CORE, together with its high resolution over a wide frequency range, will provide a more accurate estimate of the CMB dipole. The extension of boosting effects to polarization and cross-correlations will enable a more robust determination of purely velocity-driven effects that are not degenerate with the intrinsic CMB dipole, allowing us to achieve a S/N ratio of 13; this improves on the Planck detection and essentially equals that of an ideal cosmic-variance-limited experiment up to a multipole l of 2000. Precise inter-frequency calibration will offer the opportunity to constrain or even detect CMB spectral distortions, particularly from the cosmological reionization, because of the frequency dependence of the dipole spectrum, without resorting to precise absolute calibration. The expected improvement with respect to COBE-FIRAS in the recovery of distortion parameters (in principle, a factor of several hundred for an ideal experiment with the CORE configuration) ranges from a factor of several up to about 50, depending on the quality of foreground removal and relative calibration. Even for 1% accuracy in both foreground removal and relative calibration at an angular scale of 1 deg, we find that dipole analyses for a mission like CORE will be able to improve the recovery of the CIB spectrum amplitude by a factor of 17 in comparison with current results based on FIRAS. In addition to the scientific potential of a mission like CORE for these analyses, synergies with other planned and ongoing projects are also discussed. ## Authors C. Burigana, C. S. Carvalho, T. Trombetti, A. Notari, M. Quartin, G. De Gasperis, A. Buzzelli, N. Vittorio, G. De Zotti, P. de Bernardis, J. Chluba, M. Bilicki, L. Danese, J. Delabrouille, L. Toffolatti, A. Lapi, M. Negrello, P. Mazzotta, D. Scott, D. Contreras, A. Achucarro, P. Ade, R. Allison, M. Ashdown, M. Ballardini, A. J. Banday, R. Banerji, J. Bartlett, N. Bartolo, S. Basak, M. Bersanelli, A. Bonaldi, M. Bonato, J. Borrill, F. Bouchet, F. Boulanger, T. Brinckmann, M. Bucher, P. Cabella, Z. -Y. Cai, M. Calvo, G. Castellano, A. Challinor, S. Clesse, I. Colantoni, A. Coppolecchia, M. Crook, G. D'Alessandro, J. -M. Diego, A. Di Marco, E. Di Valentino, J. Errard, S. Feeney, R. Fernandez-Cobos, S. Ferraro, F. Finelli, F. Forastieri, S. Galli, R. Genova-Santos, M. Gerbino, J. Gonzalez-Nuevo, S. Grandis, J. Greenslade, S. Hagstotz, S. Hanany, W. Handley, C. Hernandez-Monteagudo, C. Hervias-Caimapo, M. Hills, E. Hivon, K. Kiiveri, T. Kisner, T. Kitching, M. Kunz, H. Kurki-Suonio, L. Lamagna, A. Lasenby, M. Lattanzi, J. Lesgourgues, M. Liguori, V. Lindholm, M. Lopez-Caniego, G. Luzzi, B. Maffei, N. Mandolesi, E. Martinez-Gonzalez, C. J. A. P. Martins, S. Masi, D. McCarthy, A. Melchiorri, J. -B. Melin, D. Molinari, A. Monfardini, P. Natoli, A. Paiella, D. Paoletti, G. Patanchon, M. Piat, G. Pisano, L. Polastri, G. Polenta, A. Pollo, V. Poulin, M. Remazeilles, M. Roman, J. -A. Rubino-Martin, L. Salvati, A. Tartari, M. Tomasi, D. Tramonte, N. Trappe, C. Tucker, J. Valiviita, R. Van de Weijgaert, B. van Tent, V. Vennin, P. Vielva, K. Young, M. Zannoni ## Published 2017-04-19T15:03:53Z # Exploring cosmic origins with CORE: mitigation of systematic effects [1707.04224](entry.id) ## Abstract We present an analysis of the main systematic effects that could impact the measurement of CMB polarization with the proposed CORE space mission. We employ timeline-to-map simulations to verify that the CORE instrumental set-up and scanning strategy allow us to measure sky polarization to a level of accuracy adequate to the mission science goals. We also show how the CORE observations can be processed to mitigate the level of contamination by potentially worrying systematics, including intensity-to-polarization leakage due to bandpass mismatch, asymmetric main beams, pointing errors and correlated noise. We use analysis techniques that are well validated on data from current missions such as Planck to demonstrate how the residual contamination of the measurements by these effects can be brought to a level low enough not to hamper the scientific capability of the mission, nor significantly increase the overall error budget. We also present a prototype of the CORE photometric calibration pipeline, based on that used for Planck, and discuss its robustness to systematics, showing how CORE can achieve its calibration requirements. While a fine-grained assessment of the impact of systematics requires a level of knowledge of the system that can only be achieved in a future study phase, the analysis presented here strongly suggests that the main areas of concern for the CORE mission can be addressed using existing knowledge, techniques and algorithms. ## Authors P. Natoli, M. Ashdown, R. Banerji, J. Borrill, A. Buzzelli, G. de Gasperis, J. Delabrouille, E. Hivon, D. Molinari, G. Patanchon, L. Polastri, M. Tomasi, F. R. Bouchet, S. Henrot-Versillé, D. T. Hoang, R. Keskitalo, K. Kiiveri, T. Kisner, V. Lindholm, D. McCarthy, F. Piacentini, O. Perdereau, G. Polenta, M. Tristram, A. Achucarro, P. Ade, R. Allison, C. Baccigalupi, M. Ballardini, A. J. Banday, J. Bartlett, N. Bartolo, S. Basak, J. Baselmans, D. Baumann, M. Bersanelli, A. Bonaldi, M. Bonato, F. Boulanger, T. Brinckmann, M. Bucher, C. Burigana, Z. -Y. Cai, M. Calvo, C. -S. Carvalho, G. Castellano, A. Challinor, J. Chluba, S. Clesse, I. Colantoni, A. Coppolecchia, M. Crook, G. D'Alessandro, P. de Bernardis, G. De Zotti, E. Di Valentino, J. -M. Diego, J. Errard, S. Feeney, R. Fernandez-Cobos, F. Finelli, F. Forastieri, S. Galli, R. Genova-Santos, M. Gerbino, J. Gonzalez-Nuevo, S. Grandis, J. Greenslade, A. Gruppuso, S. Hagstotz, S. Hanany, W. Handley, C. Hernandez-Monteagudo, C. Hervias-Caimapo, M. Hills, E. Keihänen, T. Kitching, M. Kunz, H. Kurki-Suonio, L. Lamagna, A. Lasenby, M. Lattanzi, J. Lesgourgues, A. Lewis, M. Liguori, M. López-Caniego, G. Luzzi, B. Maffei, N. Mandolesi, E. Martinez-Gonzalez, C. J. A. P. Martins, S. Masi, A. Melchiorri, J. -B. Melin, M. Migliaccio, A. Monfardini, M. Negrello, A. Notari, L. Pagano, A. Paiella, D. Paoletti, M. Piat, G. Pisano, A. Pollo, V. Poulin, M. Quartin, M. Remazeilles, M. Roman, G. Rossi, J. -A. Rubino-Martin, L. Salvati, G. Signorelli, A. Tartari, D. Tramonte, N. Trappe, T. Trombetti, C. Tucker, J. Valiviita, R. Van de Weijgaert, B. van Tent, V. Vennin, P. Vielva, N. Vittorio, C. Wallis, K. Young, M. Zannoni ## Published 2017-07-13T17:02:10Z # Dynamical dark energy in light of the latest observations [1701.08165](entry.id) ## Abstract A flat Friedman-Roberson-Walker universe dominated by a cosmological constant ($\Lambda$) and cold dark matter (CDM) has been the working model preferred by cosmologists since the discovery of cosmic acceleration. However, tensions of various degrees of significance are known to be present among existing datasets within the $\Lambda$CDM framework. In particular, the Lyman-$\alpha$ forest measurement of the Baryon Acoustic Oscillations (BAO) by the Baryon Oscillation Spectroscopic Survey (BOSS) prefers a smaller value of the matter density fraction $\Omega_{\rm M}$ compared to the value preferred by cosmic microwave background (CMB). Also, the recently measured value of the Hubble constant, $H_0=73.24\pm1.74 \ {\rm km}\ {\rm s}^{-1} \ {\rm Mpc}^{-1}$, is $3.4\sigma$ higher than $66.93\pm0.62 \ {\rm km}\ {\rm s}^{-1} \ {\rm Mpc}^{-1}$ inferred from the Planck CMB data. In this work, we investigate if these tensions can be interpreted as evidence for a non-constant dynamical dark energy (DE). Using the Kullback-Leibler (KL) divergence to quantify the tension between datasets, we find that the tensions are relieved by an evolving DE, with the dynamical DE model preferred at a $3.5\sigma$ significance level based on the improvement in the fit alone. While, at present, the Bayesian evidence for the dynamical DE is insufficient to favour it over $\Lambda$CDM, we show that, if the current best fit DE happened to be the true model, it would be decisively detected by the upcoming DESI survey. ## Authors Gong-Bo Zhao, Marco Raveri, Levon Pogosian, Yuting Wang, Robert G. Crittenden, Will J. Handley, Will J. Percival, Florian Beutler, Jonathan Brinkmann, Chia-Hsun Chuang, Antonio J. Cuesta, Daniel J. Eisenstein, Francisco-Shu Kitaura, Kazuya Koyama, Benjamin L'Huillier, Robert C. Nichol, Matthew M. Pieri, Sergio Rodriguez-Torres, Ashley J. Ross, Graziano Rossi, Ariel G. Sánchez, Arman Shafieloo, Jeremy L. Tinker, Rita Tojeiro, Jose A. Vazquez, Hanyu Zhang ## Published 2017-01-27T19:00:03Z # Exploring cosmic origins with CORE: gravitational lensing of the CMB [1707.02259](entry.id) ## Abstract Lensing of the CMB is now a well-developed probe of large-scale clustering over a broad range of redshifts. By exploiting the non-Gaussian imprints of lensing in the polarization of the CMB, the CORE mission can produce a clean map of the lensing deflections over nearly the full-sky. The number of high-S/N modes in this map will exceed current CMB lensing maps by a factor of 40, and the measurement will be sample-variance limited on all scales where linear theory is valid. Here, we summarise this mission product and discuss the science that it will enable. For example, the summed mass of neutrinos will be determined to an accuracy of 17 meV combining CORE lensing and CMB two-point information with contemporaneous BAO measurements, three times smaller than the minimum total mass allowed by neutrino oscillations. In the search for B-mode polarization from primordial gravitational waves with CORE, lens-induced B-modes will dominate over instrument noise, limiting constraints on the gravitational wave power spectrum amplitude. With lensing reconstructed by CORE, one can "delens" the observed polarization internally, reducing the lensing B-mode power by 60%. This improves to 70% by combining lensing and CIB measurements from CORE, reducing the error on the gravitational wave amplitude by 2.5 compared to no delensing (in the null hypothesis). Lensing measurements from CORE will allow calibration of the halo masses of the 40000 galaxy clusters that it will find, with constraints dominated by the clean polarization-based estimators. CORE can accurately remove Galactic emission from CMB maps with its 19 frequency channels. We present initial findings that show that residual Galactic foreground contamination will not be a significant source of bias for lensing power spectrum measurements with CORE. [abridged] ## Authors Anthony Challinor, Rupert Allison, Julien Carron, Josquin Errard, Stephen Feeney, Thomas Kitching, Julien Lesgourgues, Antony Lewis, Íñigo Zubeldía, Ana Achucarro, Peter Ade, Mark Ashdown, Mario Ballardini, A. J. Banday, Ranajoy Banerji, James Bartlett, Nicola Bartolo, Soumen Basak, Daniel Baumann, Marco Bersanelli, Anna Bonaldi, Matteo Bonato, Julian Borrill, François Bouchet, François Boulanger, Thejs Brinckmann, Martin Bucher, Carlo Burigana, Alessandro Buzzelli, Zhen-Yi Cai, Martino Calvo, Carla-Sofia Carvalho, Gabriella Castellano, Jens Chluba, Sebastien Clesse, Ivan Colantoni, Alessandro Coppolecchia, Martin Crook, Giuseppe d'Alessandro, Paolo de Bernardis, Giancarlo de Gasperis, Gianfranco De Zotti, Jacques Delabrouille, Eleonora Di Valentino, Jose-Maria Diego, Raul Fernandez-Cobos, Simone Ferraro, Fabio Finelli, Francesco Forastieri, Silvia Galli, Ricardo Genova-Santos, Martina Gerbino, Joaquin González-Nuevo, Sebastian Grandis, Joshua Greenslade, Steffen Hagstotz, Shaul Hanany, Will Handley, Carlos Hernandez-Monteagudo, Carlos Hervías-Caimapo, Matthew Hills, Eric Hivon, Kimmo Kiiveri, Ted Kisner, Martin Kunz, Hannu Kurki-Suonio, Luca Lamagna, Anthony Lasenby, Massimiliano Lattanzi, Michele Liguori, Valtteri Lindholm, Marcos López-Caniego, Gemma Luzzi, Bruno Maffei, Enrique Martinez-González, C. J. A. P. Martins, Silvia Masi, Darragh McCarthy, Alessandro Melchiorri, Jean-Baptiste Melin, Diego Molinari, Alessandro Monfardini, Paolo Natoli, Mattia Negrello, Alessio Notari, Alessandro Paiella, Daniela Paoletti, Guillaume Patanchon, Michel Piat, Giampaolo Pisano, Linda Polastri, Gianluca Polenta, Agnieszka Pollo, Vivian Poulin, Miguel Quartin, Mathieu Remazeilles, Matthieu Roman, Jose-Alberto Rubino-Martin, Laura Salvati, Andrea Tartari, Maurizio Tomasi, Denis Tramonte, Neil Trappe, Tiziana Trombetti, Carole Tucker, Jussi Valiviita, Rien Van de Weijgaert, Bartjan van Tent, Vincent Vennin, Patricio Vielva, Nicola Vittorio, Karl Young, Mario Zannoni ## Published 2017-07-07T16:37:38Z # Exploring Cosmic Origins with CORE: B-mode Component Separation [1704.04501](entry.id) ## Abstract We demonstrate that, for the baseline design of the CORE satellite mission, the polarized foregrounds can be controlled at the level required to allow the detection of the primordial cosmic microwave background (CMB) $B$-mode polarization with the desired accuracy at both reionization and recombination scales, for tensor-to-scalar ratio values of ${r\gtrsim 5\times 10^{-3}}$. We consider detailed sky simulations based on state-of-the-art CMB observations that consist of CMB polarization with $\tau=0.055$ and tensor-to-scalar values ranging from $r=10^{-2}$ to $10^{-3}$, Galactic synchrotron, and thermal dust polarization with variable spectral indices over the sky, polarized anomalous microwave emission, polarized infrared and radio sources, and gravitational lensing effects. Using both parametric and blind approaches, we perform full component separation and likelihood analysis of the simulations, allowing us to quantify both uncertainties and biases on the reconstructed primordial $B$-modes. Under the assumption of perfect control of lensing effects, CORE would measure an unbiased estimate of $r=\left(5 \pm 0.4\right)\times 10^{-3}$ after foreground cleaning. In the presence of both gravitational lensing effects and astrophysical foregrounds, the significance of the detection is lowered, with CORE achieving a $4\sigma$-measurement of $r=5\times 10^{-3}$ after foreground cleaning and $60$% delensing. For lower tensor-to-scalar ratios ($r=10^{-3}$) the overall uncertainty on $r$ is dominated by foreground residuals, not by the 40% residual of lensing cosmic variance. Moreover, the residual contribution of unprocessed polarized point-sources can be the dominant foreground contamination to primordial B-modes at this $r$ level, even on relatively large angular scales, $\ell \sim 50$. Finally, we report two sources of potential bias for the detection of the primordial $B$-modes.[abridged] ## Authors M. Remazeilles, A. J. Banday, C. Baccigalupi, S. Basak, A. Bonaldi, G. De Zotti, J. Delabrouille, C. Dickinson, H. K. Eriksen, J. Errard, R. Fernandez-Cobos, U. Fuskeland, C. Hervías-Caimapo, M. López-Caniego, E. Martinez-González, M. Roman, P. Vielva, I. Wehus, A. Achucarro, P. Ade, R. Allison, M. Ashdown, M. Ballardini, R. Banerji, N. Bartolo, J. Bartlett, D. Baumann, M. Bersanelli, M. Bonato, J. Borrill, F. Bouchet, F. Boulanger, T. Brinckmann, M. Bucher, C. Burigana, A. Buzzelli, Z. -Y. Cai, M. Calvo, C. -S. Carvalho, G. Castellano, A. Challinor, J. Chluba, S. Clesse, I. Colantoni, A. Coppolecchia, M. Crook, G. D'Alessandro, P. de Bernardis, G. de Gasperis, J. -M. Diego, E. Di Valentino, S. Feeney, S. Ferraro, F. Finelli, F. Forastieri, S. Galli, R. Genova-Santos, M. Gerbino, J. González-Nuevo, S. Grandis, J. Greenslade, S. Hagstotz, S. Hanany, W. Handley, C. Hernandez-Monteagudo, M. Hills, E. Hivon, K. Kiiveri, T. Kisner, T. Kitching, M. Kunz, H. Kurki-Suonio, L. Lamagna, A. Lasenby, M. Lattanzi, J. Lesgourgues, A. Lewis, M. Liguori, V. Lindholm, G. Luzzi, B. Maffei, C. J. A. P. Martins, S. Masi, D. McCarthy, J. -B. Melin, A. Melchiorri, D. Molinari, A. Monfardini, P. Natoli, M. Negrello, A. Notari, A. Paiella, D. Paoletti, G. Patanchon, M. Piat, G. Pisano, L. Polastri, G. Polenta, A. Pollo, V. Poulin, M. Quartin, J. -A. Rubino-Martin, L. Salvati, A. Tartari, M. Tomasi, D. Tramonte, N. Trappe, T. Trombetti, C. Tucker, J. Valiviita, R. Van de Weijgaert, B. van Tent, V. Vennin, N. Vittorio, K. Young, M. Zannoni ## Published 2017-04-14T18:00:01Z # Exploring Cosmic Origins with CORE: Survey requirements and mission design [1706.04516](entry.id) ## Abstract Future observations of cosmic microwave background (CMB) polarisation have the potential to answer some of the most fundamental questions of modern physics and cosmology. In this paper, we list the requirements for a future CMB polarisation survey addressing these scientific objectives, and discuss the design drivers of the CORE space mission proposed to ESA in answer to the "M5" call for a medium-sized mission. The rationale and options, and the methodologies used to assess the mission's performance, are of interest to other future CMB mission design studies. CORE is designed as a near-ultimate CMB polarisation mission which, for optimal complementarity with ground-based observations, will perform the observations that are known to be essential to CMB polarisation scienceand cannot be obtained by any other means than a dedicated space mission. ## Authors J. Delabrouille, P. de Bernardis, F. R. Bouchet, A. Achúcarro, P. A. R. Ade, R. Allison, F. Arroja, E. Artal, M. Ashdown, C. Baccigalupi, M. Ballardini, A. J. Banday, R. Banerji, D. Barbosa, J. Bartlett, N. Bartolo, S. Basak, J. J. A. Baselmans, K. Basu, E. S. Battistelli, R. Battye, D. Baumann, A. Benoît, M. Bersanelli, A. Bideaud, M. Biesiada, M. Bilicki, A. Bonaldi, M. Bonato, J. Borrill, F. Boulanger, T. Brinckmann, M. L. Brown, M. Bucher, C. Burigana, A. Buzzelli, G. Cabass, Z. -Y. Cai, M. Calvo, A. Caputo, C. -S. Carvalho, F. J. Casas, G. Castellano, A. Catalano, A. Challinor, I. Charles, J. Chluba, D. L. Clements, S. Clesse, S. Colafrancesco, I. Colantoni, D. Contreras, A. Coppolecchia, M. Crook, G. D'Alessandro, G. D'Amico, A. da Silva, M. de Avillez, G. de Gasperis, M. De Petris, G. de Zotti, L. Danese, F. -X. Désert, V. Desjacques, E. Di Valentino, C. Dickinson, J. M. Diego, S. Doyle, R. Durrer, C. Dvorkin, H. -K. Eriksen, J. Errard, S. Feeney, R. Fernández-Cobos, F. Finelli, F. Forastieri, C. Franceschet, U. Fuskeland, S. Galli, R. T. Génova-Santos, M. Gerbino, E. Giusarma, A. Gomez, J. González-Nuevo, S. Grandis, J. Greenslade, J. Goupy, S. Hagstotz, S. Hanany, W. Handley, S. Henrot-Versillé, C. Hernández-Monteagudo, C. Hervias-Caimapo, M. Hills, M. Hindmarsh, E. Hivon, D. T. Hoang, D. C. Hooper, B. Hu, E. Keihänen, R. Keskitalo, K. Kiiveri, T. Kisner, T. Kitching, M. Kunz, H. Kurki-Suonio, G. Lagache, L. Lamagna, A. Lapi, A. Lasenby, M. Lattanzi, A. M. C. Le Brun, J. Lesgourgues, M. Liguori, V. Lindholm, J. Lizarraga, G. Luzzi, J. F. Macìas-Pérez, B. Maffei, N. Mandolesi, S. Martin, E. Martinez-Gonzalez, C. J. A. P. Martins, S. Masi, M. Massardi, S. Matarrese, P. Mazzotta, D. McCarthy, A. Melchiorri, J. -B. Melin, A. Mennella, J. Mohr, D. Molinari, A. Monfardini, L. Montier, P. Natoli, M. Negrello, A. Notari, F. Noviello, F. Oppizzi, C. O'Sullivan, L. Pagano, A. Paiella, E. Pajer, D. Paoletti, S. Paradiso, R. B. Partridge, G. Patanchon, S. P. Patil, O. Perdereau, F. Piacentini, M. Piat, G. Pisano, L. Polastri, G. Polenta, A. Pollo, N. Ponthieu, V. Poulin, D. Prêle, M. Quartin, A. Ravenni, M. Remazeilles, A. Renzi, C. Ringeval, D. Roest, M. Roman, B. F. Roukema, J. -A. Rubino-Martin, L. Salvati, D. Scott, S. Serjeant, G. Signorelli, A. A. Starobinsky, R. Sunyaev, C. Y. Tan, A. Tartari, G. Tasinato, L. Toffolatti, M. Tomasi, J. Torrado, D. Tramonte, N. Trappe, S. Triqueneaux, M. Tristram, T. Trombetti, M. Tucci, C. Tucker, J. Urrestilla, J. Väliviita, R. Van de Weygaert, B. Van Tent, V. Vennin, L. Verde, G. Vermeulen, P. Vielva, N. Vittorio, F. Voisin, C. Wallis, B. Wandelt, I. Wehus, J. Weller, K. Young, M. Zannoni ## Published 2017-06-14T14:38:33Z # Exploring Cosmic Origins with CORE: The Instrument [1705.02170](entry.id) ## Abstract We describe a space-borne, multi-band, multi-beam polarimeter aiming at a precise and accurate measurement of the polarization of the Cosmic Microwave Background. The instrument is optimized to be compatible with the strict budget requirements of a medium-size space mission within the Cosmic Vision Programme of the European Space Agency. The instrument has no moving parts, and uses arrays of diffraction-limited Kinetic Inductance Detectors to cover the frequency range from 60 GHz to 600 GHz in 19 wide bands, in the focal plane of a 1.2 m aperture telescope cooled at 40 K, allowing for an accurate extraction of the CMB signal from polarized foreground emission. The projected CMB polarization survey sensitivity of this instrument, after foregrounds removal, is 1.7 {\mu}K$\cdot$arcmin. The design is robust enough to allow, if needed, a downscoped version of the instrument covering the 100 GHz to 600 GHz range with a 0.8 m aperture telescope cooled at 85 K, with a projected CMB polarization survey sensitivity of 3.2 {\mu}K$\cdot$arcmin. ## Authors P. de Bernardis, P. A. R. Ade, J. J. A. Baselmans, E. S. Battistelli, A. Benoit, M. Bersanelli, A. Bideaud, M. Calvo, F. J. Casas, G. Castellano, A. Catalano, I. Charles, I. Colantoni, F. Columbro, A. Coppolecchia, M. Crook, G. D'Alessandro, M. De Petris, J. Delabrouille, S. Doyle, C. Franceschet, A. Gomez, J. Goupy, S. Hanany, M. Hills, L. Lamagna, J. Macias-Perez, B. Maffei, S. Martin, E. Martinez-Gonzalez, S. Masi, D. McCarthy, A. Mennella, A. Monfardini, F. Noviello, A. Paiella, F. Piacentini, M. Piat, G. Pisano, G. Signorelli, C. Y. Tan, A. Tartari, N. Trappe, S. Triqueneaux, C. Tucker, G. Vermeulen, K. Young, M. Zannoni, A. Achúcarro, R. Allison, M. Ashdown, M. Ballardini, A. J. Banday, R. Banerji, J. Bartlett, N. Bartolo, S. Basak, A. Bonaldi, M. Bonato, J. Borrill, F. Bouchet, F. Boulanger, T. Brinckmann, M. Bucher, C. Burigana, A. Buzzelli, Z. Y. Cai, C. S. Carvalho, A. Challinor, J. Chluba, S. Clesse, G. De Gasperis, G. De Zotti, E. Di Valentino, J. M. Diego, J. Errard, S. Feeney, R. Fernandez-Cobos, F. Finelli, F. Forastieri, S. Galli, R. Génova-Santos, M. Gerbino, J. González-Nuevo, S. Hagstotz, J. Greenslade, W. Handley, C. Hernández-Monteagudo, C. Hervias-Caimapo, E. Hivon, K. Kiiveri, T. Kisner, T. Kitching, M. Kunz, H. Kurki-Suonio, A. Lasenby, M. Lattanzi, J. Lesgourgues, A. Lewis, M. Liguori, V. Lindholm, G. Luzzi, C. J. A. P. Martins, A. Melchiorri, J. B. Melin, D. Molinari, P. Natoli, M. Negrello, A. Notari, D. Paoletti, G. Patanchon, L. Polastri, G. Polenta, A. Pollo, V. Poulin, M. Quartin, M. Remazeilles, M. Roman, J. A. Rubiño-Martín, L. Salvati, M. Tomasi, D. Tramonte, T. Trombetti, J. Väliviita, R. Van de Weijgaert, B. van Tent, V. Vennin, P. Vielva, N. Vittorio ## Published 2017-05-05T11:10:04Z # Exploring Cosmic Origins with CORE: Extragalactic sources in Cosmic Microwave Background maps [1609.07263](entry.id) ## Abstract We discuss the potential of a next generation space-borne Cosmic Microwave Background (CMB) experiment for studies of extragalactic sources. Our analysis has particular bearing on the definition of the future space project, CORE, that has been submitted in response to ESA's call for a Medium-size mission opportunity as the successor of the Planck satellite. Even though the effective telescope size will be somewhat smaller than that of Planck, CORE will have a considerably better angular resolution at its highest frequencies, since, in contrast with Planck, it will be diffraction limited at all frequencies. The improved resolution implies a considerable decrease of the source confusion, i.e. substantially fainter detection limits. In particular, CORE will detect thousands of strongly lensed high-z galaxies distributed over the full sky. The extreme brightness of these galaxies will make it possible to study them, via follow-up observations, in extraordinary detail. Also, the CORE resolution matches the typical sizes of high-z galaxy proto-clusters much better than the Planck resolution, resulting in a much higher detection efficiency; these objects will be caught in an evolutionary phase beyond the reach of surveys in other wavebands. Furthermore, CORE will provide unique information on the evolution of the star formation in virialized groups and clusters of galaxies up to the highest possible redshifts. Finally, thanks to its very high sensitivity, CORE will detect the polarized emission of thousands of radio sources and, for the first time, of dusty galaxies, at mm and sub-mm wavelengths, respectively. ## Authors G. De Zotti, J. Gonzalez-Nuevo, M. Lopez-Caniego, M. Negrello, J. Greenslade, C. Hernandez-Monteagudo, J. Delabrouille, Z. -Y. Cai, M. Bonato, A. Achucarro, P. Ade, R. Allison, M. Ashdown, M. Ballardini, A. J. Banday, R. Banerji, J. G. Bartlett, N. Bartolo, S. Basak, M. Bersanelli, M. Biesiada, M. Bilicki, A. Bonaldi, J. Borrill, F. Bouchet, F. Boulanger, T. Brinckmann, M. Bucher, C. Burigana, A. Buzzelli, M. Calvo, C. S. Carvalho, M. G. Castellano, A. Challinor, J. Chluba, D. L. Clements, S. Clesse, S. Colafrancesco, I. Colantoni, A. Coppolecchia, M. Crook, G. D'Alessandro, P. de Bernardis, G. de Gasperis, J. M. Diego, E. Di Valentino, J. Errard, S. M. Feeney, R. Fernandez-Cobos, S. Ferraro, F. Finelli, F. Forastieri, S. Galli, R. T. Genova-Santos, M. Gerbino, S. Grandis, S. Hagstotz, S. Hanany, W. Handley, C. Hervias-Caimapo, M. Hills, E. Hivon, K. Kiiveri, T. Kisner, T. Kitching, M. Kunz, H. Kurki-Suonio, G. Lagache, L. Lamagna, A. Lasenby, M. Lattanzi, A. Le Brun, J. Lesgourgues, A. Lewis, M. Liguori, V. Lindholm, G. Luzzi, B. Maffei, N. Mandolesi, E. Martinez-Gonzalez, C. J. A. P. Martins, S. Masi, M. Massardi, D. McCarthy, A. Melchiorri, J. -B. Melin, D. Molinari, A. Monfardini, P. Natoli, A. Notari, A. Paiella, D. Paoletti, R. B. Partridge, G. Patanchon, M. Piat, G. Pisano, L. Polastri, G. Polenta, A. Pollo, V. Poulin, M. Quartin, M. Remazeilles, M. Roman, G. Rossi, B. F. Roukema, J. -A. Rubino-Martin, L. Salvati, D. Scott, S. Serjeant, A. Tartari, L. Toffolatti, M. Tomasi, N. Trappe, S. Triqueneaux, T. Trombetti, M. Tucci, C. Tucker, J. Valiviita, R. van de Weygaert, B. Van Tent, V. Vennin, P. Vielva, N. Vittorio, K. Young ## Published 2016-09-23T08:02:59Z # Exploring Cosmic Origins with CORE: Cosmological Parameters [1612.00021](entry.id) ## Abstract We forecast the main cosmological parameter constraints achievable with the CORE space mission which is dedicated to mapping the polarisation of the Cosmic Microwave Background (CMB). CORE was recently submitted in response to ESA's fifth call for medium-sized mission proposals (M5). Here we report the results from our pre-submission study of the impact of various instrumental options, in particular the telescope size and sensitivity level, and review the great, transformative potential of the mission as proposed. Specifically, we assess the impact on a broad range of fundamental parameters of our Universe as a function of the expected CMB characteristics, with other papers in the series focusing on controlling astrophysical and instrumental residual systematics. In this paper, we assume that only a few central CORE frequency channels are usable for our purpose, all others being devoted to the cleaning of astrophysical contaminants. On the theoretical side, we assume LCDM as our general framework and quantify the improvement provided by CORE over the current constraints from the Planck 2015 release. We also study the joint sensitivity of CORE and of future Baryon Acoustic Oscillation and Large Scale Structure experiments like DESI and Euclid. Specific constraints on the physics of inflation are presented in another paper of the series. In addition to the six parameters of the base LCDM, which describe the matter content of a spatially flat universe with adiabatic and scalar primordial fluctuations from inflation, we derive the precision achievable on parameters like those describing curvature, neutrino physics, extra light relics, primordial helium abundance, dark matter annihilation, recombination physics, variation of fundamental constants, dark energy, modified gravity, reionization and cosmic birefringence. (ABRIDGED) ## Authors Eleonora Di Valentino, Thejs Brinckmann, Martina Gerbino, Vivian Poulin, François R. Bouchet, Julien Lesgourgues, Alessandro Melchiorri, Jens Chluba, Sebastien Clesse, Jacques Delabrouille, Cora Dvorkin, Francesco Forastieri, Silvia Galli, Deanna C. Hooper, Massimiliano Lattanzi, Carlos J. A. P. Martins, Laura Salvati, Giovanni Cabass, Andrea Caputo, Elena Giusarma, Eric Hivon, Paolo Natoli, Luca Pagano, Simone Paradiso, Jose Alberto Rubino-Martin, Ana Achucarro, Peter Ade, Rupert Allison, Frederico Arroja, Marc Ashdown, Mario Ballardini, A. J. Banday, Ranajoy Banerji, Nicola Bartolo, James G. Bartlett, Soumen Basak, Jochem Baselmans, Daniel Baumann, Paolo de Bernardis, Marco Bersanelli, Anna Bonaldi, Matteo Bonato, Julian Borrill, François Boulanger, Martin Bucher, Carlo Burigana, Alessandro Buzzelli, Zhen-Yi Cai, Martino Calvo, Carla Sofia Carvalho, Gabriella Castellano, Anthony Challinor, Ivan Charles, Ivan Colantoni, Alessandro Coppolecchia, Martin Crook, Giuseppe D'Alessandro, Marco De Petris, Gianfranco De Zotti, Josè Maria Diego, Josquin Errard, Stephen Feeney, Raul Fernandez-Cobos, Simone Ferraro, Fabio Finelli, Giancarlo de Gasperis, Ricardo T. Génova-Santos, Joaquin González-Nuevo, Sebastian Grandis, Josh Greenslade, Steffen Hagstotz, Shaul Hanany, Will Handley, Dhiraj K. Hazra, Carlos Hernández-Monteagudo, Carlos Hervias-Caimapo, Matthew Hills, Kimmo Kiiveri, Ted Kisner, Thomas Kitching, Martin Kunz, Hannu Kurki-Suonio, Luca Lamagna, Anthony Lasenby, Antony Lewis, Michele Liguori, Valtteri Lindholm, Marcos Lopez-Caniego, Gemma Luzzi, Bruno Maffei, Sylvain Martin, Enrique Martinez-Gonzalez, Silvia Masi, Darragh McCarthy, Jean-Baptiste Melin, Joseph J. Mohr, Diego Molinari, Alessandro Monfardini, Mattia Negrello, Alessio Notari, Alessandro Paiella, Daniela Paoletti, Guillaume Patanchon, Francesco Piacentini, Michael Piat, Giampaolo Pisano, Linda Polastri, Gianluca Polenta, Agnieszka Pollo, Miguel Quartin, Mathieu Remazeilles, Matthieu Roman, Christophe Ringeval, Andrea Tartari, Maurizio Tomasi, Denis Tramonte, Neil Trappe, Tiziana Trombetti, Carole Tucker, Jussi Väliviita, Rien van de Weygaert, Bartjan Van Tent, Vincent Vennin, Gérard Vermeulen, Patricio Vielva, Nicola Vittorio, Karl Young, Mario Zannoni ## Published 2016-11-30T21:00:06Z # Exploring Cosmic Origins with CORE: Inflation [1612.08270](entry.id) ## Abstract We forecast the scientific capabilities to improve our understanding of cosmic inflation of CORE, a proposed CMB space satellite submitted in response to the ESA fifth call for a medium-size mission opportunity. The CORE satellite will map the CMB anisotropies in temperature and polarization in 19 frequency channels spanning the range 60-600 GHz. CORE will have an aggregate noise sensitivity of $1.7 \mu$K$\cdot \,$arcmin and an angular resolution of 5' at 200 GHz. We explore the impact of telescope size and noise sensitivity on the inflation science return by making forecasts for several instrumental configurations. This study assumes that the lower and higher frequency channels suffice to remove foreground contaminations and complements other related studies of component separation and systematic effects, which will be reported in other papers of the series "Exploring Cosmic Origins with CORE." We forecast the capability to determine key inflationary parameters, to lower the detection limit for the tensor-to-scalar ratio down to the $10^{-3}$ level, to chart the landscape of single field slow-roll inflationary models, to constrain the epoch of reheating, thus connecting inflation to the standard radiation-matter dominated Big Bang era, to reconstruct the primordial power spectrum, to constrain the contribution from isocurvature perturbations to the $10^{-3}$ level, to improve constraints on the cosmic string tension to a level below the presumptive GUT scale, and to improve the current measurements of primordial non-Gaussianities down to the $f_{NL}^{\rm local} < 1$ level. For all the models explored, CORE alone will improve significantly on the present constraints on the physics of inflation. Its capabilities will be further enhanced by combining with complementary future cosmological observations. ## Authors CORE Collaboration, Fabio Finelli, Martin Bucher, Ana Achúcarro, Mario Ballardini, Nicola Bartolo, Daniel Baumann, Sébastien Clesse, Josquin Errard, Will Handley, Mark Hindmarsh, Kimmo Kiiveri, Martin Kunz, Anthony Lasenby, Michele Liguori, Daniela Paoletti, Christophe Ringeval, Jussi Väliviita, Bartjan van Tent, Vincent Vennin, Rupert Allison, Frederico Arroja, Marc Ashdown, A. J. Banday, Ranajoy Banerji, James G. Bartlett, Soumen Basak, Jochem Baselmans, Paolo de Bernardis, Marco Bersanelli, Anna Bonaldi, Julian Borril, François R. Bouchet, François Boulanger, Thejs Brinckmann, Carlo Burigana, Alessandro Buzzelli, Zhen-Yi Cai, Martino Calvo, Carla Sofia Carvalho, Gabriella Castellano, Anthony Challinor, Jens Chluba, Ivan Colantoni, Martin Crook, Giuseppe D'Alessandro, Guido D'Amico, Jacques Delabrouille, Vincent Desjacques, Gianfranco De Zotti, Jose Maria Diego, Eleonora Di Valentino, Stephen Feeney, James R. Fergusson, Raul Fernandez-Cobos, Simone Ferraro, Francesco Forastieri, Silvia Galli, Juan García-Bellido, Giancarlo de Gasperis, Ricardo T. Génova-Santos, Martina Gerbino, Joaquin González-Nuevo, Sebastian Grandis, Josh Greenslade, Steffen Hagstotz, Shaul Hanany, Dhiraj K. Hazra, Carlos Hernández-Monteagudo, Carlos Hervias-Caimapo, Matthew Hills, Eric Hivon, Bin Hu, Ted Kisner, Thomas Kitching, Ely D. Kovetz, Hannu Kurki-Suonio, Luca Lamagna, Massimiliano Lattanzi, Julien Lesgourgues, Antony Lewis, Valtteri Lindholm, Joanes Lizarraga, Marcos López-Caniego, Gemma Luzzi, Bruno Maffei, Nazzareno Mandolesi, Enrique Martínez-González, Carlos J. A. P. Martins, Silvia Masi, Darragh McCarthy, Sabino Matarrese, Alessandro Melchiorri, Jean-Baptiste Melin, Diego Molinari, Alessandro Monfardini, Paolo Natoli, Mattia Negrello, Alessio Notari, Filippo Oppizzi, Alessandro Paiella, Enrico Pajer, Guillaume Patanchon, Subodh P. Patil, Michael Piat, Giampaolo Pisano, Linda Polastri, Gianluca Polenta, Agnieszka Pollo, Vivian Poulin, Miguel Quartin, Andrea Ravenni, Mathieu Remazeilles, Alessandro Renzi, Diederik Roest, Matthieu Roman, Jose Alberto Rubiño-Martin, Laura Salvati, Alexei A. Starobinsky, Andrea Tartari, Gianmassimo Tasinato, Maurizio Tomasi, Jesús Torrado, Neil Trappe, Tiziana Trombetti, Carole Tucker, Marco Tucci, Jon Urrestilla, Rien van de Weygaert, Patricio Vielva, Nicola Vittorio, Karl Young ## Published 2016-12-25T14:36:35Z # Exploring Cosmic Origins with CORE: Cluster Science [1703.10456](entry.id) ## Abstract We examine the cosmological constraints that can be achieved with a galaxy cluster survey with the future CORE space mission. Using realistic simulations of the millimeter sky, produced with the latest version of the Planck Sky Model, we characterize the CORE cluster catalogues as a function of the main mission performance parameters. We pay particular attention to telescope size, key to improved angular resolution, and discuss the comparison and the complementarity of CORE with ambitious future ground-based CMB experiments that could be deployed in the next decade. A possible CORE mission concept with a 150 cm diameter primary mirror can detect of the order of 50,000 clusters through the thermal Sunyaev-Zeldovich effect (SZE). The total yield increases (decreases) by 25% when increasing (decreasing) the mirror diameter by 30 cm. The 150 cm telescope configuration will detect the most massive clusters ($>10^{14}\, M_\odot$) at redshift $z>1.5$ over the whole sky, although the exact number above this redshift is tied to the uncertain evolution of the cluster SZE flux-mass relation; assuming self-similar evolution, CORE will detect $\sim 500$ clusters at redshift $z>1.5$. This changes to 800 (200) when increasing (decreasing) the mirror size by 30 cm. CORE will be able to measure individual cluster halo masses through lensing of the cosmic microwave background anisotropies with a 1-$\sigma$ sensitivity of $4\times10^{14} M_\odot$, for a 120 cm aperture telescope, and $10^{14} M_\odot$ for a 180 cm one. [abridged] ## Authors J. -B. Melin, A. Bonaldi, M. Remazeilles, S. Hagstotz, J. M. Diego, C. Hernández-Monteagudo, R. T. Génova-Santos, G. Luzzi, C. J. A. P. Martins, S. Grandis, J. J. Mohr, J. G. Bartlett, J. Delabrouille, S. Ferraro, D. Tramonte, J. A. Rubiño-Martín, J. F. Macìas-Pérez, A. Achúcarro, P. Ade, R. Allison, M. Ashdown, M. Ballardini, A. J. Banday, R. Banerji, N. Bartolo, S. Basak, J. Baselmans, K. Basu, R. A. Battye, D. Baumann, M. Bersanelli, M. Bonato, J. Borrill, F. Bouchet, F. Boulanger, T. Brinckmann, M. Bucher, C. Burigana, A. Buzzelli, Z. -Y. Cai, M. Calvo, C. S. Carvalho, M. G. Castellano, A. Challinor, J. Chluba, S. Clesse, S. Colafrancesco, I. Colantoni, A. Coppolecchia, M. Crook, G. D'Alessandro, P. de Bernardis, G. de Gasperis, M. De Petris, G. De Zotti, E. Di Valentino, J. Errard, S. M. Feeney, R. Fernández-Cobos, F. Finelli, F. Forastieri, S. Galli, M. Gerbino, J. González-Nuevo, J. Greenslade, S. Hanany, W. Handley, C. Hervias-Caimapo, M. Hills, E. Hivon, K. Kiiveri, T. Kisner, T. Kitching, M. Kunz, H. Kurki-Suonio, L. Lamagna, A. Lasenby, M. Lattanzi, A. M. C. Le Brun, J. Lesgourgues, A. Lewis, M. Liguori, V. Lindholm, M. Lopez-Caniego, B. Maffei, E. Martinez-Gonzalez, S. Masi, D. McCarthy, A. Melchiorri, D. Molinari, A. Monfardini, P. Natoli, M. Negrello, A. Notari, A. Paiella, D. Paoletti, G. Patanchon, M. Piat, G. Pisano, L. Polastri, G. Polenta, A. Pollo, V. Poulin, M. Quartin, M. Roman, L. Salvati, A. Tartari, M. Tomasi, N. Trappe, S. Triqueneaux, T. Trombetti, C. Tucker, J. Väliviita, R. van de Weygaert, B. Van Tent, V. Vennin, P. Vielva, N. Vittorio, J. Weller, K. Young, M. Zannoni ## Published 2017-03-30T13:15:52Z # Constraining the dark energy equation of state using Bayes theorem and the Kullback-Leibler divergence [1607.00270](entry.id) ## Abstract Data-driven model-independent reconstructions of the dark energy equation of state $w(z)$ are presented using Planck 2015 era CMB, BAO, SNIa and Lyman-$\alpha$ data. These reconstructions identify the $w(z)$ behaviour supported by the data and show a bifurcation of the equation of state posterior in the range $1.5{<}z{<}3$. Although the concordance $\Lambda$CDM model is consistent with the data at all redshifts in one of the bifurcated spaces, in the other a supernegative equation of state (also known as `phantom dark energy') is identified within the $1.5 \sigma$ confidence intervals of the posterior distribution. To identify the power of different datasets in constraining the dark energy equation of state, we use a novel formulation of the Kullback--Leibler divergence. This formalism quantifies the information the data add when moving from priors to posteriors for each possible dataset combination. The SNIa and BAO datasets are shown to provide much more constraining power in comparison to the Lyman-$\alpha$ datasets. Further, SNIa and BAO constrain most strongly around redshift range $0.1-0.5$, whilst the Lyman-$\alpha$ data constrains weakly over a broader range. We do not attribute the supernegative favouring to any particular dataset, and note that the $\Lambda$CDM model was favoured at more than $2$ log-units in Bayes factors over all the models tested despite the weakly preferred $w(z)$ structure in the data. ## Authors S. Hee, J. A. Vázquez, W. J. Handley, M. P. Hobson, A. N. Lasenby ## Published 2016-07-01T14:54:32Z # Bayesian model selection without evidences: application to the dark energy equation-of-state [1506.09024](entry.id) ## Abstract A method is presented for Bayesian model selection without explicitly computing evidences, by using a combined likelihood and introducing an integer model selection parameter $n$ so that Bayes factors, or more generally posterior odds ratios, may be read off directly from the posterior of $n$. If the total number of models under consideration is specified a priori, the full joint parameter space $(\theta, n)$ of the models is of fixed dimensionality and can be explored using standard Markov chain Monte Carlo (MCMC) or nested sampling methods, without the need for reversible jump MCMC techniques. The posterior on $n$ is then obtained by straightforward marginalisation. We demonstrate the efficacy of our approach by application to several toy models. We then apply it to constraining the dark energy equation-of-state using a free-form reconstruction technique. We show that $\Lambda$CDM is significantly favoured over all extensions, including the simple $w(z){=}{\rm constant}$ model. ## Authors Sonke Hee, Will Handley, Mike P. Hobson, Anthony N. Lasenby ## Published 2015-06-30T10:45:24Z # The Runge-Kutta-Wentzel-Kramers-Brillouin Method [1612.02288](entry.id) ## Abstract We demonstrate the effectiveness of a novel scheme for numerically solving linear differential equations whose solutions exhibit extreme oscillation. We take a standard Runge-Kutta approach, but replace the Taylor expansion formula with a Wentzel-Kramers-Brillouin method. The method is demonstrated by application to the Airy equation, along with a more complicated burst-oscillation case. Finally, we compare our scheme to existing approaches. ## Authors W. J. Handley, A. N. Lasenby, M. P. Hobson ## Published 2016-12-03T12:26:06Z # Novel quantum initial conditions for inflation [1607.04148](entry.id) ## Abstract We present a novel approach for setting initial conditions on the mode functions of the Mukhanov Sazaki equation. These conditions are motivated by minimisation of the renormalised stress-energy tensor, and are valid for setting a vacuum state even in a context where the spacetime is changing rapidly. Moreover, these alternative conditions are potentially observationally distinguishable. We apply this to the kinetically dominated universe, and compare with the more traditional approach. ## Authors W. J. Handley, A. N. Lasenby, M. P. Hobson ## Published 2016-07-14T14:28:13Z # AMI observations of ten CLASH galaxy clusters: SZ and X-ray data used together to determine cluster dynamical states [1604.06120](entry.id) ## Abstract Using Arcminute Microkelvin Imager (AMI) SZ observations towards ten CLASH clusters we investigate the influence of cluster mergers on observational galaxy cluster studies. Although selected to be largely relaxed, there is disagreement in the literature on the dynamical states of CLASH sample members. We analyse our AMI data in a fully Bayesian way to produce estimated cluster parameters and consider the intrinsic correlations in our NFW/GNFW-based model. Varying pressure profile shape parameters, illustrating an influence of mergers on scaling relations, induces small deviations from the canonical self-similar predictions -- in agreement with simulations of Poole et al. 2007 who found that merger activity causes only small scatter perpendicular to the relations. We demonstrate this effect observationally using the different dependencies of SZ and X-ray signals to $n_{\rm e}$ that cause different sensitivities to the shocking and/or fractionation produced by mergers. Plotting $Y_{\rm X}$--$M_{\rm gas}$ relations (where $Y_{\rm X}=M_{\rm gas}T$) derived from AMI SZ and from $Chandra$ X-ray gives ratios of AMI and $Chandra$ $Y_{\rm X}$ and $M_{\rm gas}$ estimates that indicate movement of clusters \textit{along} the scaling relation, as predicted by Poole et al. 2007. Clusters that have moved most along the relation have the most discrepant $T_{\rm SZ}$ and $T_{\rm X}$ estimates: all the other clusters (apart from one) have SZ and X-ray estimates of $M_{\rm gas}$, $T$ and $Y_{\rm X}$ that agree within $r_{500}$. We use SZ vs X-ray discrepancies in conjunction with $Chandra$ maps and $T_{\rm X}$ profiles, making comparisons with simulated cluster merger maps in Poole et al. 2006, to identify disturbed members of our sample and estimate merger stages. ## Authors Clare Rumsey, Malak Olamaie, Yvette C. Perrott, Helen R. Russell, Farhan Feroz, Keith J. B. Grainge, Will J. Handley, Michael P. Hobson, Richard D. E. Saunders, Michel P. Schammel ## Published 2016-04-20T20:35:40Z # Planck 2015 results. I. Overview of products and scientific results [1502.01582](entry.id) ## Abstract The European Space Agency's Planck satellite, dedicated to studying the early Universe and its subsequent evolution, was launched 14~May 2009 and scanned the microwave and submillimetre sky continuously between 12~August 2009 and 23~October 2013. In February~2015, ESA and the Planck Collaboration released the second set of cosmology products based on data from the entire Planck mission, including both temperature and polarization, along with a set of scientific and technical papers and a web-based explanatory supplement. This paper gives an overview of the main characteristics of the data and the data products in the release, as well as the associated cosmological and astrophysical science results and papers. The science products include maps of the cosmic microwave background (CMB), the thermal Sunyaev-Zeldovich effect, and diffuse foregrounds in temperature and polarization, catalogues of compact Galactic and extragalactic sources (including separate catalogues of Sunyaev-Zeldovich clusters and Galactic cold clumps), and extensive simulations of signals and noise used in assessing the performance of the analysis methods and assessment of uncertainties. The likelihood code used to assess cosmological models against the Planck data are described, as well as a CMB lensing likelihood. Scientific results include cosmological parameters deriving from CMB power spectra, gravitational lensing, and cluster counts, as well as constraints on inflation, non-Gaussianity, primordial magnetic fields, dark energy, and modified gravity. ## Authors Planck Collaboration, R. Adam, P. A. R. Ade, N. Aghanim, Y. Akrami, M. I. R. Alves, M. Arnaud, F. Arroja, J. Aumont, C. Baccigalupi, M. Ballardini, A. J. Banday, R. B. Barreiro, J. G. Bartlett, N. Bartolo, S. Basak, P. Battaglia, E. Battaner, R. Battye, K. Benabed, A. Benoît, A. Benoit-Lévy, J. -P. Bernard, M. Bersanelli, B. Bertincourt, P. Bielewicz, A. Bonaldi, L. Bonavera, J. R. Bond, J. Borrill, F. R. Bouchet, F. Boulanger, M. Bucher, C. Burigana, R. C. Butler, E. Calabrese, J. -F. Cardoso, P. Carvalho, B. Casaponsa, G. Castex, A. Catalano, A. Challinor, A. Chamballu, R. -R. Chary, H. C. Chiang, J. Chluba, P. R. Christensen, S. Church, M. Clemens, D. L. Clements, S. Colombi, L. P. L. Colombo, C. Combet, B. Comis, D. Contreras, F. Couchot, A. Coulais, B. P. Crill, M. Cruz, A. Curto, F. Cuttaia, L. Danese, R. D. Davies, R. J. Davis, P. de Bernardis, A. de Rosa, G. de Zotti, J. Delabrouille, J. -M. Delouis, F. -X. Désert, E. Di Valentino, C. Dickinson, J. M. Diego, K. Dolag, H. Dole, S. Donzelli, O. Doré, M. Douspis, A. Ducout, J. Dunkley, X. Dupac, G. Efstathiou, P. R. M. Eisenhardt, F. Elsner, T. A. Enßlin, H. K. Eriksen, E. Falgarone, Y. Fantaye, M. Farhang, S. Feeney, J. Fergusson, R. Fernandez-Cobos, F. Feroz, F. Finelli, E. Florido, O. Forni, M. Frailis, A. A. Fraisse, C. Franceschet, E. Franceschi, A. Frejsel, A. Frolov, S. Galeotta, S. Galli, K. Ganga, C. Gauthier, R. T. Génova-Santos, M. Gerbino, T. Ghosh, M. Giard, Y. Giraud-Héraud, E. Giusarma, E. Gjerløw, J. González-Nuevo, K. M. Górski, K. J. B. Grainge, S. Gratton, A. Gregorio, A. Gruppuso, J. E. Gudmundsson, J. Hamann, W. Handley, F. K. Hansen, D. Hanson, D. L. Harrison, A. Heavens, G. Helou, S. Henrot-Versillé, C. Hernández-Monteagudo, D. Herranz, S. R. Hildebrandt, E. Hivon, M. Hobson, W. A. Holmes, A. Hornstrup, W. Hovest, Z. Huang, K. M. Huffenberger, G. Hurier, S. Ilić, A. H. Jaffe, T. R. Jaffe, T. Jin, W. C. Jones, M. Juvela, A. Karakci, E. Keihänen, R. Keskitalo, K. Kiiveri, J. Kim, T. S. Kisner, R. Kneissl, J. Knoche, N. Krachmalnicoff, M. Kunz, H. Kurki-Suonio, F. Lacasa, G. Lagache, A. Lähteenmäki, J. -M. Lamarre, M. Langer, A. Lasenby, M. Lattanzi, C. R. Lawrence, M. Le Jeune, J. P. Leahy, E. Lellouch, R. Leonardi, J. León-Tavares, J. Lesgourgues, F. Levrier, A. Lewis, M. Liguori, P. B. Lilje, M. Linden-Vørnle, V. Lindholm, H. Liu, M. López-Caniego, P. M. Lubin, Y. -Z. Ma, J. F. Macías-Pérez, G. Maggio, D. S. Y. Mak, N. Mandolesi, A. Mangilli, A. Marchini, A. Marcos-Caballero, D. Marinucci, D. J. Marshall, P. G. Martin, M. Martinelli, E. Martínez-González, S. Masi, S. Matarrese, P. Mazzotta, J. D. McEwen, P. McGehee, S. Mei, P. R. Meinhold, A. Melchiorri, J. -B. Melin, L. Mendes, A. Mennella, M. Migliaccio, K. Mikkelsen, S. Mitra, M. -A. Miville-Deschênes, D. Molinari, A. Moneti, L. Montier, R. Moreno, G. Morgante, D. Mortlock, A. Moss, S. Mottet, M. Müenchmeyer, D. Munshi, J. A. Murphy, A. Narimani, P. Naselsky, A. Nastasi, F. Nati, P. Natoli, M. Negrello, C. B. Netterfield, H. U. Nørgaard-Nielsen, F. Noviello, D. Novikov, I. Novikov, M. Olamaie, N. Oppermann, E. Orlando, C. A. Oxborrow, F. Paci, L. Pagano, F. Pajot, R. Paladini, S. Pandolfi, D. Paoletti, B. Partridge, F. Pasian, G. Patanchon, T. J. Pearson, M. Peel, H. V. Peiris, V. -M. Pelkonen, O. Perdereau, L. Perotto, Y. C. Perrott, F. Perrotta, V. Pettorino, F. Piacentini, M. Piat, E. Pierpaoli, D. Pietrobon, S. Plaszczynski, D. Pogosyan, E. Pointecouteau, G. Polenta, L. Popa, G. W. Pratt, G. Prézeau, S. Prunet, J. -L. Puget, J. P. Rachen, B. Racine, W. T. Reach, R. Rebolo, M. Reinecke, M. Remazeilles, C. Renault, A. Renzi, I. Ristorcelli, G. Rocha, M. Roman, E. Romelli, C. Rosset, M. Rossetti, A. Rotti, G. Roudier, B. Rouillé d'Orfeuil, M. Rowan-Robinson, J. A. Rubiño-Martín, B. Ruiz-Granados, C. Rumsey, B. Rusholme, N. Said, V. Salvatelli, L. Salvati, M. Sandri, H. S. Sanghera, D. Santos, R. D. E. Saunders, A. Sauvé, M. Savelainen, G. Savini, B. M. Schaefer, M. P. Schammel, D. Scott, M. D. Seiffert, P. Serra, E. P. S. Shellard, T. W. Shimwell, M. Shiraishi, K. Smith, T. Souradeep, L. D. Spencer, M. Spinelli, S. A. Stanford, D. Stern, V. Stolyarov, R. Stompor, A. W. Strong, R. Sudiwala, R. Sunyaev, P. Sutter, D. Sutton, A. -S. Suur-Uski, J. -F. Sygnet, J. A. Tauber, D. Tavagnacco, L. Terenzi, D. Texier, L. Toffolatti, M. Tomasi, M. Tornikoski, M. Tristram, A. Troja, T. Trombetti, M. Tucci, J. Tuovinen, M. Türler, G. Umana, L. Valenziano, J. Valiviita, B. Van Tent, T. Vassallo, M. Vidal, M. Viel, P. Vielva, F. Villa, L. A. Wade, B. Walter, B. D. Wandelt, R. Watson, I. K. Wehus, N. Welikala, J. Weller, M. White, S. D. M. White, A. Wilkinson, D. Yvon, A. Zacchei, J. P. Zibin, A. Zonca ## Published 2015-02-05T15:08:26Z # PolyChord: next-generation nested sampling [1506.00171](entry.id) ## Abstract PolyChord is a novel nested sampling algorithm tailored for high-dimensional parameter spaces. This paper coincides with the release of PolyChord v1.3, and provides an extensive account of the algorithm. PolyChord utilises slice sampling at each iteration to sample within the hard likelihood constraint of nested sampling. It can identify and evolve separate modes of a posterior semi-independently, and is parallelised using openMPI. It is capable of exploiting a hierarchy of parameter speeds such as those present in CosmoMC and CAMB, and is now in use in the CosmoChord and ModeChord codes. PolyChord is available for download at: http://ccpforge.cse.rl.ac.uk/gf/project/polychord/ ## Authors W. J. Handley, M. P. Hobson, A. N. Lasenby ## Published 2015-05-30T22:17:35Z # PolyChord: nested sampling for cosmology [1502.01856](entry.id) ## Abstract PolyChord is a novel nested sampling algorithm tailored for high dimensional parameter spaces. In addition, it can fully exploit a hierarchy of parameter speeds such as is found in CosmoMC and CAMB. It utilises slice sampling at each iteration to sample within the hard likelihood constraint of nested sampling. It can identify and evolve separate modes of a posterior semi-independently and is parallelised using openMPI. PolyChord is available for download at: http://ccpforge.cse.rl.ac.uk/gf/project/polychord/ ## Authors W. J. Handley, M. P. Hobson, A. N. Lasenby ## Published 2015-02-06T10:59:22Z ``` 2. **Research Group Structure:** ```yaml Adam Ormondroyd: image: images/adam_ormondroyd.jpg links: GitHub: https://github.com/AdamOrmondroyd linkedin: https://www.linkedin.com/in/adam-ormondroyd/ original_image: images/originals/adam_ormondroyd.jpg phd: start: 2021-10-01 supervisors: - Mike Hobson - Will Handley - Anthony Lasenby thesis: null Aleksandr Petrosyan: destination: 2020-10-01: Lead cryptography engineer, Armenia image: images/aleksandr_petrosyan.jpg original_image: images/originals/aleksandr_petrosyan.jpeg partiii: end: 2020-06-01 start: 2019-10-01 supervisors: - Will Handley thesis: Accelerated nested sampling in the context of cosmological parameter estimation Allahyar Sahibzada: image: images/allahyar_sahibzada.jpg mphil: end: 2022-12-19 start: 2021-10-01 supervisors: - Will Handley thesis: 'Machine Learning and Nested Sampling: in the context of data intensive science and cosmology' original_image: images/originals/allahyar_sahibzada.jpeg Anastasia Fialkov: coi: start: 2019-10-01 thesis: null image: https://www.ast.cam.ac.uk/sites/default/files/styles/inline/public/anastasia-fialkov-20180213-sq2.jpg?itok=am4DF9YQ links: Department webpage: https://www.ast.cam.ac.uk/people/Anastasia.Fialkov Anthony Lasenby: coi: start: 2012-10-01 thesis: null image: https://www.phy.cam.ac.uk/sites/default/files/styles/leading/public/media/profile/lasenbya.jpg?itok=9nNfXc4k links: Department webpage: https://www.phy.cam.ac.uk/directory/lasenbya Artyom Baryshnikov: destination: 2022-10-01: MSc in Cyber Security in Edinburgh image: images/artyom_baryshnikov.jpg links: linkedin: https://www.linkedin.com/in/artem-baryshnikov-4b31a6189 original_image: images/originals/artyom_baryshnikov.png summer: end: 2022-08-26 start: 2022-06-27 thesis: null Ayngaran Thavanesan: image: images/ayngaran_thavanesan.jpg original_image: images/originals/ayngaran_thavanesan.png phd: end: 2023-01-19 start: 2021-10-01 supervisors: - David Stefanyszyn - Will Handley thesis: null Beichen Xu: destination: 2022-10-01: Physics in Birmingham image: images/beichen_xu.jpg original_image: images/originals/beichen_xu.jpg summer: end: 2022-09-16 start: 2022-06-27 thesis: null Bob Knighton: destination: 2019-10-01: PhD in theoretical cosmology, ETH Zurich 2023-10-01: Postdoc at DAMTP (Cambridge) image: images/bob_knighton.jpg original_image: images/originals/bob_knighton.JPG partiii: end: 2017-06-01 start: 2016-10-01 supervisors: - Will Handley thesis: Investigations into the Kinetically Dominated Universe Carola Zanoletti: destination: 2022-10-01: PhD in cosmology, Nottingham image: images/carola_zanoletti.jpg links: Group webpage: https://blogs.ncl.ac.uk/cosmology/ PhD project: https://research.ncl.ac.uk/phdstudentships/robinsoncosmology/#Leonard PhD supervisor: https://www.mas.ncl.ac.uk/danielle.leonard/ original_image: images/originals/carola_zanoletti.jpg partiii: end: 2022-06-01 start: 2021-10-01 supervisors: - Will Handley thesis: 'Palindromic Universes: Alternative Solution by Matrix Representation' Charlotte Priestley: image: images/charlotte_priestley.jpg original_image: images/originals/charlotte_priestley.jpg partiii: start: 2024-10-01 supervisors: - Will Handley - Harry Bevins thesis: null summer: end: 2024-08-30 start: 2024-07-01 supervisors: - Harry Bevins thesis: null Chris Lester: coi: start: 2023-10-01 thesis: null image: https://www.phy.cam.ac.uk/sites/default/files/styles/leading/public/media/profile/lesterc.jpg?itok=QNLbVvIS links: Department webpage: https://www.phy.cam.ac.uk/directory/lesterc Cole Meldorf: image: images/cole_meldorf.jpg links: Google scholar: https://scholar.google.com/citations?user=Zqa8QOMAAAAJ&hl=en&oi=ao original_image: images/originals/cole_meldorf.jpg partiii: end: 2023-06-01 start: 2022-10-01 supervisors: - Will Handley thesis: Bayesian inference and the shape of the primordial universe Daniel Manela: destination: 2019-10-01: Msc Computational stats & ML, UCL 2021-01-01: statistical/ML engineer at UCB Pharmaceuticals 2022-10-01: PhD in ML, Oxford image: images/daniel_manela.jpg links: Department webpage: https://csml.stats.ox.ac.uk/ original_image: images/originals/daniel_manela.png partiii: end: 2017-06-01 start: 2016-10-01 supervisors: - Will Handley thesis: Affine-invariant ensemble sampling with applications to LIGO data Danielle Dineen: destination: 2023-10-01: PhD in Cosmology, Toronto image: images/danielle_dineen.jpg links: arxiv papers: https://arxiv.org/search/?query=danielle+dineen&searchtype=all&source=header linkedin: https://www.linkedin.com/in/danielle-dineen-34887a120/ mphil: end: 2023-09-15 start: 2022-10-01 supervisors: - Will Handley thesis: Cosmological Matching Conditions for Primordial Perturbations original_image: images/originals/danielle_dineen.jpg David Stefanyszyn: coi: start: 2021-10-01 thesis: null links: Department webpage: https://www.nottingham.ac.uk/physics/people/david.stefanyszyn David Yallup: image: images/david_yallup.jpg links: ORCiD: https://orcid.org/0000-0003-4716-5817 linkedin: https://www.linkedin.com/in/dyallup/ original_image: images/originals/david_yallup.jpg postdoc: start: 2021-01-10 thesis: null Deaglan Bartlett: destination: 2019-10-01: PhD in Astrophysics, Oxford 2022-10-01: Postdoc in IAP, Paris image: images/deaglan_bartlett.jpg links: Webpage: https://www.physics.ox.ac.uk/our-people/bartlett arXiv: https://arxiv.org/a/bartlett_d_1 original_image: images/originals/deaglan_bartlett.JPG partiii: end: 2019-06-01 start: 2018-10-01 supervisors: - Will Handley thesis: The Conformal Boundary at the End of the Universe Denis Werth: destination: 2019-10-01: Masters in Sorbonne, Paris 2021-10-01: PhD in Astrophysics, Paris (IAP & Sorbonne) image: images/denis_werth.jpg original_image: images/originals/denis_werth.jpg summer: end: 2019-09-01 start: 2019-06-01 thesis: null Dily Ong: image: images/dily_ong.jpg original_image: images/originals/dily_ong.jpg phd: start: 2023-10-01 supervisors: - Will Handley thesis: null Dominic Anstey: destination: 2022-10-01: Postdoc at Cambridge (UK) image: images/dominic_anstey.jpg original_image: images/originals/dominic_anstey.jpg phd: end: 2022-09-30 start: 2018-10-01 supervisors: - Eloy de Lera Acedo - Will Handley thesis: 'Data Analysis in Global 21cm Experiments: Physically Motivated Bayesian Modelling Techniques' Ed Higson: destination: 2017-10-01: Goldman Sachs (UK finance) 2020-05-01: DE Shaw (US finance) image: images/ed_higson.jpg links: linkedin: https://www.linkedin.com/in/ejhigson original_image: images/originals/ed_higson.jpg phd: end: 2018-10-01 start: 2016-10-01 supervisors: - Will Handley - Mike Hobson - Anthony Lasenby thesis: Bayesian Methods and machine Learning in Astrophysics Elizabeth Guest: destination: 2019-10-01: MSc in Theoretical Chemistry, Cambridge 2022-10-01: PhD in exoplanet atmospheres, UCL image: images/elizabeth_guest.jpg original_image: images/originals/elizabeth_guest.jpg summer: end: 2018-09-01 start: 2018-06-01 thesis: null Eloy de Lera Acedo: coi: start: 2018-10-01 thesis: null image: https://www.astro.phy.cam.ac.uk/sites/default/files/styles/inline/public/images/profile/headshotlow.jpg?itok=RMrJ4zTa links: Department webpage: https://www.phy.cam.ac.uk/directory/dr-eloy-de-lera-acedo Emma Shen: destination: 2021-10-01: PhD in Radio astronomy, Cambridge image: images/emma_shen.jpg mphil: end: 2020-09-30 start: 2019-10-01 supervisors: - Eloy de Lera Acedo - Anastasia Fialkov - Will Handley thesis: Ionospheric Effects in the Global 21-cm Experiment original_image: images/originals/emma_shen.jpg Felicity Ibrahim: image: images/felicity_ibrahim.jpg original_image: images/originals/felicity_ibrahim.png partiii: end: 2024-06-01 start: 2023-10-01 supervisors: - Will Handley thesis: Higher order solvers for cosmological perturbations Fruzsina Agocs: destination: 2021-10-01: 3y fellowship CCM New York 2024-10-01: Assistant Professor at Boulder, Colorado image: images/fruzsina_agocs.jpg links: Group webpage: https://www.simonsfoundation.org/people/fruzsina-agocs/ Webpage: https://fruzsinaagocs.github.io/ original_image: images/originals/fruzsina_agocs.jpg partiii: end: 2017-06-01 start: 2016-10-01 supervisors: - Will Handley thesis: "The Runge\u2013Kutta\u2013Wentzel\u2013Kramers\u2013Brillouin method\ \ and the primordial Universe" phd: end: 2021-09-01 start: 2017-10-01 supervisors: - Will Handley - Anthony Lasenby - Mike Hobson thesis: 'Primordial evolution of cosmological perturbations: Theory and computation' George Carter: image: images/george_carter.jpg original_image: originals/images/george_carter.jpg phd: end: 2024-08-11 start: 2020-10-01 supervisors: - Will Handley - Nima Razavi-Ghods - Mark Ashdown thesis: The Bayesian Global Sky Model (B-GSM) postdoc: end: 2024-11-12 start: 2024-08-12 thesis: null "G\xE1bor Cs\xE1nyi": coi: start: 2023-10-01 thesis: null image: https://www.eng.cam.ac.uk/sites/www.eng.cam.ac.uk/files/styles/small_events_search_results_profile/public/uploads/profiles/images/Gabor-kalapos-square-400.png?itok=GszDCAc9 links: Department webpage: http://www.eng.cam.ac.uk/profiles/gc121 Harry Bevins: coi: start: 2023-10-01 thesis: null destination: 2023-04-01: Postdoc in Cambridge (Eloy) 2023-10-01: Cambridge Kavli Fellowship image: images/harry_bevins.jpg links: ADS: https://ui.adsabs.harvard.edu/search/q=author%3A%22Bevins%2C%20H.%20T.%20J.%22&sort=date%20desc%2C%20bibcode%20desc&p_=0 GitHub: https://github.com/htjb Publons: https://publons.com/researcher/5239833/harry-bevins/ Webpage: https://htjb.github.io/ original_image: images/originals/harry_bevins.jpeg phd: end: 2023-03-31 start: 2019-10-01 supervisors: - Will Handley - Eloy de Lera Acedo - Anastasia Fialkov thesis: A Machine Learning-enhanced Toolbox for Bayesian 21-cm Data Analysis and Constraints on the Astrophysics of the Early Universe Harvey Williams: image: images/harvey_williams.jpg original_image: images/originals/harvey_williams.jpg partiii: start: 2024-10-01 supervisors: - Will Handley thesis: null Ian Roque: destination: 2024-08-01: Stanford SLAC staff engineer image: images/ian_roque.jpg links: Webpage: https://www.astro.phy.cam.ac.uk/directory/ian-roque mphil: end: 2019-09-15 start: 2018-10-01 supervisors: - Nima Razavi-Ghods - Will Handley thesis: Bayesian Techniques for the Calibration of 21 cm Global Experiments original_image: images/originals/ian_roque.png phd: end: 2023-12-31 start: 2019-10-01 supervisors: - Will Handley - Nima Razavi-Ghods thesis: 'EXCALIBRATE: Calibration for astrophysical experimentation' Isidro Gomez Vargas: destination: 2021-11-01: Postdoc at UNAM (mexico) image: images/isidro_gomez_vargas.jpg links: Department webpage: https://www.fis.unam.mx/directorio/1333/isidro-strong-gomez-strong-vargas Webpage: https://igomezv.github.io original_image: images/originals/isidro_gomez_vargas.jpg phd: end: 2020-12-04 start: 2020-03-16 supervisors: - Jose Alberto Vazquez - Will Handley thesis: null James Alvey: coi: start: 2024-10-01 thesis: null image: https://www.kicc.cam.ac.uk/sites/default/files/styles/inline/public/images/profile/profilepicture-min_1.jpeg?itok=ccmz2RPK links: Department webpage: Department webpage Jamie Bamber: destination: 2019-10-01: PhD in Astrophysics, Oxford image: images/jamie_bamber.jpg original_image: images/originals/jamie_bamber.JPG partiii: end: 2019-06-01 start: 2018-10-01 supervisors: - Will Handley thesis: Beyond the Runge-Kutta-Wentzel-Kramers-Brillouin method Jessica Rigley: destination: 2019-10-01: PhD in astronomy, IoA image: images/jessica_rigley.jpg links: Website: https://jessicarigley.com/ original_image: images/originals/jessica_rigley.jpeg partiii: end: 2018-06-01 start: 2017-10-01 supervisors: - Will Handley thesis: Cosmologically Investigating the Neutrino Hierachy Jose Alberto Vazquez: coi: start: 2020-03-16 thesis: null links: INSPIRE: https://inspirehep.net/authors/1061596 thesis: null Kamran Javid: destination: 2019-10-01: AI Researcher (systematic trading), Arabesque AI, London 2023-01-01: Quantitative Research & Development (systematic trading), ADIA, United Arab Emirates image: images/kamran_javid.jpg links: Google scholar: https://scholar.google.com/citations?user=USKsovMAAAAJ linkedin: https://www.linkedin.com/in/kamranjavid91 original_image: images/originals/kamran_javid.jpeg phd: end: 2018-09-30 start: 2017-10-01 supervisors: - Will Handley thesis: null postdoc: end: 2019-10-01 start: 2018-10-01 thesis: null Keith Grainge: coi: start: 2020-06-10 thesis: null links: Department webpage: https://www.research.manchester.ac.uk/portal/keith.grainge.html Kilian Scheutwinkel: destination: 2024-09-01: TRGC (Venture fund focussed on digital assets) image: images/kilian_scheutwinkel.jpg links: C2D3 profile: https://www.c2d3.cam.ac.uk/directory/8681/mr-kilian-scheutwinkel Group webpage: https://www.cavendishradiocosmology.com/ original_image: images/originals/kilian_scheutwinkel.JPG phd: end: 2024-08-09 start: 2020-12-01 supervisors: - Will Handley - Eloy de Lera Acedo thesis: Simulation-based Bayesian machine learning methods for Cosmology and beyond Krish Nanavati: image: images/krish_nanavati.jpg original_image: images/originals/krish_nanavati.jpg partiii: start: 2024-10-01 supervisors: - James Alvey - Will Handley thesis: null Liam L.H. Lau: destination: 2019-10-01: PhD in Physics, Rutgers (US) image: images/liam_lau.jpg original_image: images/originals/liam_lau.jpg summer: end: 2019-09-01 start: 2019-06-01 thesis: Machine learning the future of cosmology experiments Lukas Hergt: destination: 2021-01-08: 4-year cosmology fellowship in UBC image: images/lukas_hergt.jpg links: Webpage: https://phas.ubc.ca/users/lukas-hergt original_image: images/originals/lukas_hergt.jpg phd: end: 2021-01-08 start: 2017-01-01 supervisors: - Will Handley - Anthony Lasenby - Mike Hobson thesis: null Malak Olamaie: coi: start: 2020-06-10 thesis: null links: Department webpage: https://www.yorksj.ac.uk/our-staff/staff-profiles/malak-olamaie.php Mark Ashdown: coi: start: 2021-10-01 thesis: null image: https://www.phy.cam.ac.uk/sites/default/files/styles/inline/public/images/profile/dr_mark_ashdown.png?itok=rkun0buR links: Department webpage: https://www.phy.cam.ac.uk/staff/dr-mark-ashdown Mary Letey: destination: 2022-10-01: Msc in Theoretical Physics, Perimeter Institute 2023-10-01: PhD in Applied Mathematics, Harvard image: images/mary_letey.jpg links: linkedin: https://www.linkedin.com/in/maryletey original_image: images/originals/mary_letey.jpg summer: end: 2022-08-22 start: 2022-06-24 thesis: null Mattia Varrone: image: images/mattia_varrone.jpg original_image: images/originals/mattia_varrone.jpg summer: end: 2021-09-30 start: 2021-06-21 thesis: null Maxime Jabarian: destination: 2022-01-01: AI/Cybersecurity startup, Paris image: images/maxime_jabarian.jpg links: ResearchGate: https://www.researchgate.net/profile/Maxime-Jabarian-2 linkedin: https://www.linkedin.com/in/maxime-jabarian/ original_image: images/originals/maxime_jabarian.jpeg summer: end: 2019-09-01 start: 2019-06-01 thesis: null Metha Prathaban: image: images/metha_prathaban.jpg links: GitHub: https://github.com/mrosep Harding Scholar: https://www.hardingscholars.fund.cam.ac.uk/metha-prathaban-2022-cohort original_image: images/originals/metha_prathaban.png partiii: end: 2021-06-01 start: 2020-10-01 supervisors: - Will Handley thesis: Evidence for a Palindromic Universe phd: start: 2022-10-01 supervisors: - Will Handley thesis: null Mike Hobson: coi: start: 2012-10-01 thesis: null image: https://www.phy.cam.ac.uk/sites/default/files/styles/leading/public/media/profile/hobsonm.jpg?itok=H1iEFAas links: Department webpage: https://www.phy.cam.ac.uk/directory/hobsonm Ming Yang: image: images/ming_yang.jpg original_image: images/originals/ming_yang.jpeg partiii: start: 2024-10-01 supervisors: - Will Handley thesis: null Namu Kroupa: image: images/namu_kroupa.jpg original_image: images/originals/namu_kroupa.jpg phd: start: 2023-10-01 supervisors: - "G\xE1bor Cs\xE1nyi" - Will Handley thesis: null summer: end: 2023-09-30 start: 2023-06-12 thesis: null Nicolas Mediato Diaz: partiii: end: 2024-06-01 start: 2023-10-01 supervisors: - Will Handley thesis: Astronomical Linear Simulation-based Inference summer: end: 2024-09-13 start: 2024-07-22 thesis: null Nima Razavi-Ghods: coi: start: 2019-10-01 thesis: null links: Department webpage: https://www.phy.cam.ac.uk/directory/razavi-ghods Oliver Normand: destination: 2022-10-01: Management consultancy image: images/oliver_normand.jpg original_image: images/originals/oliver_normand.jpg partiii: end: 2022-06-01 start: 2021-10-01 supervisors: - Will Handley thesis: Bayesian reconstructions of the primordial universe from Planck CMB data Panagiotis Mavrogiannis: destination: 2018-10-01: PhD in Astrophysics, Thessaloniki, Greece image: images/panagiotis_mavrogiannis.jpg mphil: end: 2018-09-30 start: 2017-10-01 supervisors: - Anthony Lasenby - Will Handley thesis: "Wheeler\u2013Feynman absorber theory of radiation: Establishing the cosmological\ \ electrodynamic arrow of time" original_image: images/originals/panagiotis_mavrogiannis.jpg Patrick Lau: partiii: end: 2024-06-01 start: 2023-10-01 supervisors: - Will Handley thesis: null Sam Leeney: image: images/sam_leeney.jpg links: Group Webpage: https://www.cavendishradiocosmology.com/ Webpage: https://github.com/samleeney mphil: end: 2022-12-30 start: 2022-04-11 supervisors: - Eloy de Lera Acedo thesis: 'Data science in early universe Cosmology: a novel Bayesian RFI mitigation approach using numerical sampling techniques' original_image: images/originals/sam_leeney.jpeg phd: start: 2023-10-01 supervisors: - Eloy de Lera Acedo - Harry Bevins - Will Handley thesis: null Samuel Hewson: partiii: end: 2024-06-01 start: 2023-10-01 supervisors: - Will Handley thesis: Galaxies, snails and parity violation summer: end: 2024-08-01 start: 2024-06-24 supervisors: - Chris Lester thesis: null Sankalan Bhattacharyya: image: images/sankalan_bhattacharyya.jpg original_image: images/originals/sankalan_bhattacharyya.jpg partiii: end: 2023-06-01 start: 2022-10-01 supervisors: - Will Handley thesis: Jordan-Magnus Methods for Cosmological Perturbation Theory Shu-Fan Chen: destination: 2019-10-01: PhD in Cosmology, Harvard image: images/shu-fan_chen.jpg original_image: images/originals/shu-fan_chen.jpeg summer: end: 2018-09-01 start: 2018-06-01 thesis: null Sinah Legner: image: images/sinah_legner.jpg original_image: images/originals/sinah_legner.jpg phd: start: 2022-10-01 supervisors: - Will Handley - Will Barker thesis: null Stephen Pickman: destination: 2017-10-01: Software developer at DarkTrace image: images/stephen_pickman.jpg original_image: images/originals/stephen_pickman.jpeg partiii: end: 2017-06-01 start: 2016-10-01 supervisors: - Will Handley thesis: The perfect clustering algorithm Suhail Dhawan: coi: start: 2024-10-01 thesis: null image: https://www.lucy.cam.ac.uk/sites/default/files/styles/650x650_scale_and_crop/public/fellow-images/Suhail%20Dhawan.jpg?itok=IinGhbdp links: Department webpage: https://www.lucy.cam.ac.uk/fellows/dr-suhail-dhawan Thomas Gessey-Jones: destination: 2024-08-05: PhysicsX image: images/thomas_gessey-jones.jpg links: Group webpage: https://www.cavendishradiocosmology.com/ arXiv: https://arxiv.org/search/?query=T+Gessey-Jones&searchtype=all&abstracts=show&order=-announced_date_first&size=50 original_image: images/originals/thomas_gessey-jones.jpg partiii: end: 2020-06-01 start: 2019-10-01 supervisors: - Will Handley thesis: Initial Conditions Before Inflation phd: end: 2024-03-31 start: 2020-10-01 supervisors: - Eloy de Lera Acedo - Anastasia Fialkov - Will Handley thesis: 'Probing the First Stars with the 21-cm Signal: Theory, Methods, and Forecasts' postdoc: end: 2024-08-04 start: 2024-04-01 thesis: null Thomas Mcaloone: destination: 2021-10-01: Data scientist (PolyChord Ltd) image: images/thomas_mcaloone.jpg original_image: images/originals/thomas_mcaloone.jpg phd: end: 2021-09-30 start: 2020-06-10 supervisors: - Keith Grainge - Malak Olamaie - Will Handley thesis: null Toby Lovick: image: images/toby_lovick.jpg original_image: images/originals/toby_lovick.jpeg partiii: end: 2023-06-01 start: 2022-10-01 supervisors: - Suhail Dhawan - Will Handley thesis: null phd: start: 2024-10-01 supervisors: - Will Handley thesis: null summer: end: 2023-09-15 start: 2023-07-24 supervisors: - Suhail Dhawan thesis: null Tze Goh: image: images/tze_goh.jpg original_image: images/originals/tze_goh.jpeg partiii: end: 2024-06-01 start: 2023-10-01 supervisors: - Suhail Dhawan - Will Handley thesis: 'Bayesian Model Selection of Anisotropic Cosmologies with Type Ia supernova data ' Ward Haddadin: destination: 2018-10-01: PhD in Particle physics theory, DAMTP image: images/ward_haddadin.jpg original_image: images/originals/ward_haddadin.jpg partiii: end: 2018-06-01 start: 2017-10-01 supervisors: - Will Handley thesis: The Primordial Power Spectrum of Kinetically Dominated Universes summer: end: 2018-09-01 start: 2018-06-01 thesis: null Wei-Ning Deng: image: images/wei-ning_deng.jpg original_image: images/originals/wei-ning_deng.jpg phd: start: 2022-10-01 supervisors: - Will Handley thesis: null Will Barker: coi: start: 2022-10-01 thesis: null destination: 2021-10-01: 3y Junior Research Fellowship (Girton, Cambridge) 2024-10-01: 2y Marie Curie fellowship prague image: images/will_barker.jpg links: Webpage: https://wevbarker.com original_image: images/originals/will_barker.png phd: end: 2021-08-25 start: 2017-10-01 supervisors: - Anthony Lasenby - Mike Hobson - Will Handley thesis: null Will Handley: image: images/will_handley.jpg links: Webpage: https://willhandley.co.uk original_image: images/originals/will_handley.jpeg phd: end: 2016-09-30 start: 2012-10-01 supervisors: - Anthony Lasenby - Mike Hobson thesis: 'Kinetic initial conditions for inflation: theory, observation and methods' pi: start: 2020-10-01 thesis: null postdoc: end: 2020-10-01 start: 2016-10-01 thesis: null Will Templeton: image: images/will_templeton.jpg original_image: images/originals/will_templeton.png partiii: start: 2024-10-01 supervisors: - Will Handley thesis: null Xy Wang: destination: 2022-10-01: PhD in Quantum Computing, Germany image: images/xy_wang.jpg original_image: images/originals/xy_wang.jpg partiii: end: 2022-06-01 start: 2021-10-01 supervisors: - Will Handley thesis: Accelerated nested sampling with proposal prior mixing for Bayesian inference Yi Jer Loh: destination: 2021-10-01: Data Scientist, Spotify image: images/yi_jer_loh.jpg original_image: images/originals/yi_jer_loh.jpg partiii: end: 2021-06-01 start: 2020-10-01 supervisors: - Will Handley thesis: Constructing Non-Linear Cosmological Tension Coordinate with Neural Networks Yoann Launay: destination: 2022-10-01: PhD in Cosmology, DAMTP image: images/yoann_launay.jpg original_image: images/originals/yoann_launay.jpg partiii: end: 2022-06-01 start: 2021-10-01 supervisors: - Will Handley thesis: Primordial Non-Gaussianity from kinetic initial conditions for inflation Zak Shumaylov: destination: 2022-10-01: PhD in machine learning, DAMTP image: images/zak_shumaylov.jpg original_image: images/originals/zak_shumaylov.jpeg summer: end: 2021-09-30 start: 2021-06-21 thesis: null Zixiao Hu: image: images/zixiao_hu.jpg original_image: images/originals/zixiao_hu.jpeg partiii: end: 2023-06-01 start: 2022-10-01 supervisors: - Will Handley thesis: Approximating the end of nested sampling summer: end: 2023-08-18 start: 2023-06-26 thesis: null ``` 3. **Future Research Directions (from our Grant Application):** ```tex \documentclass[11pt,a4paper]{article} \usepackage[T1]{fontenc} \renewcommand*\familydefault{\sfdefault} \usepackage{sfmath} \usepackage{amssymb} \date{} \usepackage{graphicx} \usepackage[margin=2cm,top=2cm]{geometry} \usepackage[hidelinks]{hyperref} \usepackage[capitalise]{cleveref} \newcommand{\arXiv}[1]{[{\titlecolor{}\href{https://arxiv.org/abs/#1}{#1}}]} \pdfinclusioncopyfonts=1 \usepackage{lipsum} \usepackage[dvipsnames]{xcolor} \newcommand{\titlecolor}{\color{RoyalBlue}} \title{\titlecolor{}\vspace{-50pt}Resolving the Universe with Scientific AI: \\ A New Era of Cosmological Analysis with Simulation Based Inference \vspace{-5pt}} \author{\titlecolor{}Will Handley} \begin{document} \maketitle \vspace{-5pt} This research proposal stands at the exciting frontier of cosmology, machine learning (ML), and advanced statistical inference. We are entering a new age of data-driven discovery in astrophysics, with next-generation telescopes and detectors poised to deliver datasets of unprecedented scale and precision. These advances hold the potential to address fundamental questions about our Universe, including the nature of dark matter and dark energy. This programme is particularly timely given the emergence of powerful new AI tools, such as transformers, GPT-4, Claude, and Gemini, which are poised to revolutionise both the practice and discoveries of scientific research. Historically, the analysis of cosmological data has relied on computationally expensive techniques that require simplifying assumptions. However, the complexity and volume of upcoming datasets necessitate new analysis paradigms. SBI offers a powerful alternative, leveraging scientific ability to forward simulate realistic datasets from theoretical models. This approach bypasses the need for explicitly constructing likelihood functions, which are intractable for all but the simplest systems. This is particularly relevant for incorporating systematic uncertainties and astrophysical effects that are challenging to model analytically. While SBI has shown promise in fields like particle physics, its application to cosmology is still in its nascent stages. This research programme aims to bridge this gap by developing and deploying cutting-edge SBI methodologies tailored for the analysis of next-generation cosmological surveys, including the Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations (BAO) from surveys like DESI and 4MOST, and gravitational wave observations from LIGO, Virgo, and future detectors like LISA. Our team's edge is in our experience of developing and deploying principled Bayesian inference and in understanding rather than merely using the latest AI tools. \begin{figure} \includegraphics[width=\textwidth]{images/3.png} \caption{Image generated by the DALL-E API prompted by the title of this research proposal. Whilst expressiveness like this captures the public imagination, the real power of AI is its ability to enhance scientific discovery by improving and accelerating scientific code \& writing. In addition to harnessing AI to perform fundamental science with SBI, this research programme will be powered by a fully machine-enhanced team of scientists, with funds set aside to keep the group at the rising edge of the AI wave.} \end{figure} \subsection*{\titlecolor{}Research Objectives \& Expected Outputs} This research programme will pursue the following interlinked objectives: \begin{description} \item [Beyond Likelihood:] Build next-generation physical CMB and BAO codes for the Simulation Based Inference paradigm. \begin{itemize} \item Output: Develop and publicly release software for efficient and accurate simulation of CMB and BAO datasets, incorporating realistic astrophysical effects and systematic uncertainties. This will provide the foundation for applying SBI to these key cosmological probes. \item Output: Implement and benchmark novel SBI algorithms tailored for the analysis of simulated CMB and BAO data, enabling robust parameter inference and model comparison. \end{itemize} \item [Beyond Density Estimation:] Build next-generation SBI tools. \begin{itemize} \item Output: Explore and develop advanced SBI techniques that go beyond standard density estimation approaches, focusing on neural ratio estimation (NRE) methods. These methods offer potential advantages in efficiency and scalability for high-dimensional cosmological inference problems. \item Output: Develop and disseminate software implementations of these NRE methods, making them accessible to the wider scientific community. \end{itemize} \item [Beyond Dark Matter and Dark Energy:] Extensions to Einstein's GR. \begin{itemize} \item Output: Leverage the developed SBI framework to test the standard cosmological model and explore extensions to General Relativity. This will involve incorporating modified gravity theories into the simulation pipeline and comparing their predictions against observational data. \item Output: Constrain the parameter space of a theoretically motivated selection of theories, providing insights into the nature of gravity on cosmological scales. \end{itemize} \item [Beyond Telescopes:] GAMBIT as a tool \& community for combining particle physics with cosmology. \begin{itemize} \item Output: Expand the existing GAMBIT framework to interface with the developed SBI codes, enabling joint analyses of cosmological and particle physics data. This will facilitate a more holistic understanding of the Universe's fundamental constituents and interactions. \item Output: Strengthen collaborations within the GAMBIT community and foster interdisciplinary research at the interface of cosmology and particle physics. \end{itemize} \item [Beyond Hand Calculation:] Next-generation automation of theoretical model building. \begin{itemize} \item Output: Investigate and develop novel techniques for automating the process of building and testing theoretical models using a combination of symbolic computation, large language models, and high-performance computing. \item Output: Apply these techniques to construct and constrain modified gravity models using data from GAIA and other astrophysical surveys. \end{itemize} \end{description} \subsection*{\titlecolor{}Methodology} This ambitious research programme will be realised through a multipronged approach, capitalising on the combination of next-generation datasets, cutting-edge AI techniques, and a network of world-leading collaborators. At the heart of this research lies harnessing the power of upcoming cosmological datasets. This includes analysing data from current and future Cosmic Microwave Background experiments, exploiting their sensitivity to primordial fluctuations and cosmological parameters. It also encompasses utilizing spectroscopic surveys like DESI and 4MOST which map millions of galaxies and provide exquisite measurements of Baryon Acoustic Oscillations, providing a powerful probe of dark energy. Furthermore, the research programme will prepare for the advent of gravitational wave cosmology, using data from LIGO, Virgo, and future detectors like LISA to probe gravity in extreme environments and constrain cosmological models. Of particular interest will be the use of dark sirens, bright sirens and spectral sirens - gravitational wave sources whose redshift can be independently measured - to provide powerful new constraints on cosmological models. Finally, these diverse datasets will be combined with other astrophysical probes, such as supernovae and galaxy clustering from JWST and Euclid, to obtain complementary constraints on cosmological models. Analysing these vast and complex datasets necessitates the development and deployment of advanced AI and machine learning techniques. This includes building and deploying efficient and scalable SBI algorithms tailored for cosmological data analysis. This will involve combining realistic simulations of the Universe with astrophysical systematics, and training neural networks to efficiently extract cosmological information. In addition, the programme will explore and implement cutting-edge sampling techniques, such as those based on neural ratio estimation, to improve the efficiency and scalability of Bayesian inference for high-dimensional cosmological problems. This research will be driven by a collaborative network encompassing the expertise and resources available within the University of Cambridge, a world-leading centre for cosmology, statistical inference, and machine learning. This programme will build on my team's unique strengths in Bayesian statistics and nested sampling to tackle these challenges. My team will collaborate with the international GAMBIT community to integrate the developed SBI tools into their framework, enabling joint analyses of cosmological and particle physics data. Finally, the programme will nurture the collaborations with experts I have built over the past four years in gravitational wave astronomy, large-scale structure surveys, and astrophysical modelling to ensure the research remains at the forefront of the field. By combining these elements, this research programme is well-positioned to make significant contributions to our understanding of the Universe and to push the boundaries of cosmological data analysis. \subsection*{\titlecolor{}Milestones and Timescales} \subsubsection*{Year 1: Foundations and Early Implementations} \begin{description} \item[Milestone 1] Deepen collaborations with the GAMBIT community by initiating new PhD student projects to explore the integration of developed SBI tools (by month 6). \item[Milestone 2] Implement and benchmark standard neural density estimation-based SBI algorithms for CMB and BAO data analysis (by month 9). \item[Milestone 3] Develop and publicly release a software package for simulating CMB and BAO datasets incorporating realistic astrophysical effects (by month 12). \end{description} \subsubsection*{Year 2: Advanced Algorithms and Model Building} \begin{description} \item[Milestone 4] Develop and test novel SBI algorithms based on neural ratio estimation, demonstrating improved efficiency and scalability for cosmological inference (by month 18). \item[Milestone 5] Publicly release software implementations of the developed NRE-based SBI algorithms (by month 21). \item[Milestone 6] Develop and implement automated tools for building and testing modified gravity models using symbolic computation and machine learning (by month 24). \end{description} \subsubsection*{Year 3: Scientific Exploitation and Dissemination} \begin{description} \item[Milestone 7] Apply the developed SBI framework to analyse real cosmological data from DESI and other surveys, constraining cosmological parameters and testing modified gravity models (by month 30). \item[Milestone 8] Integrate the developed SBI codes into the GAMBIT framework, enabling joint analyses of cosmological and particle physics data (by month 33). \item[Milestone 9] Disseminate research findings through peer-reviewed publications, conference presentations, and workshops (ongoing). \end{description} \end{document} ``` ==================================================================================== Final Output Requirements ==================================================================================== - Combine all data sources to create a seamless, engaging narrative. - Follow the exact Markdown output format provided at the top. - Do not include any extra explanation, commentary, or wrapping beyond the specified Markdown. - Ensure every reference to a research topic includes a correctly formatted Markdown link (e.g., [AI methodologies](https://arxiv.org/abs/2503.08658)), and validate that it corresponds to the correct paper in the list of Published papers. - Utilize all provided sources to construct a narrative that is both cohesive and faithful to our research contributions. - The tone should be professional, accessible, and engaging. Generate only the final Markdown output that meets all these requirements.