{% raw %} Title: Create a Markdown Blog Post Integrating Research Details and a Featured Paper ==================================================================================== This task involves generating a Markdown file (ready for a GitHub-served Jekyll site) that integrates our research details with a featured research paper. The output must follow the exact format and conventions described below. ==================================================================================== Output Format (Markdown): ------------------------------------------------------------------------------------ --- layout: post title: "Strengthening the bound on the mass of the lightest neutrino with terrestrial and cosmological experiments" date: 2020-09-07 categories: papers --- ![AI generated image](/assets/images/posts/2020-09-07-2009.03287.png) Will Handley Content generated by [gemini-2.5-pro](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/content/2020-09-07-2009.03287.txt). Image generated by [imagen-3.0-generate-002](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/images/2020-09-07-2009.03287.txt). ------------------------------------------------------------------------------------ ==================================================================================== Please adhere strictly to the following instructions: ==================================================================================== Section 1: Content Creation Instructions ==================================================================================== 1. **Generate the Page Body:** - Write a well-composed, engaging narrative that is suitable for a scholarly audience interested in advanced AI and astrophysics. - Ensure the narrative is original and reflective of the tone and style and content in the "Homepage Content" block (provided below), but do not reuse its content. - Use bullet points, subheadings, or other formatting to enhance readability. 2. **Highlight Key Research Details:** - Emphasize the contributions and impact of the paper, focusing on its methodology, significance, and context within current research. - Specifically highlight the lead author ({'name': 'The GAMBIT Cosmology Workgroup'}). When referencing any author, use Markdown links from the Author Information block (choose academic or GitHub links over social media). 3. **Integrate Data from Multiple Sources:** - Seamlessly weave information from the following: - **Paper Metadata (YAML):** Essential details including the title and authors. - **Paper Source (TeX):** Technical content from the paper. - **Bibliographic Information (bbl):** Extract bibliographic references. - **Author Information (YAML):** Profile details for constructing Markdown links. - Merge insights from the Paper Metadata, TeX source, Bibliographic Information, and Author Information blocks into a coherent narrative—do not treat these as separate or isolated pieces. - Insert the generated narrative between the HTML comments: and 4. **Generate Bibliographic References:** - Review the Bibliographic Information block carefully. - For each reference that includes a DOI or arXiv identifier: - For DOIs, generate a link formatted as: [10.1234/xyz](https://doi.org/10.1234/xyz) - For arXiv entries, generate a link formatted as: [2103.12345](https://arxiv.org/abs/2103.12345) - **Important:** Do not use any LaTeX citation commands (e.g., `\cite{...}`). Every reference must be rendered directly as a Markdown link. For example, instead of `\cite{mycitation}`, output `[mycitation](https://doi.org/mycitation)` - **Incorrect:** `\cite{10.1234/xyz}` - **Correct:** `[10.1234/xyz](https://doi.org/10.1234/xyz)` - Ensure that at least three (3) of the most relevant references are naturally integrated into the narrative. - Ensure that the link to the Featured paper [2009.03287](https://arxiv.org/abs/2009.03287) is included in the first sentence. 5. **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. **Homepage Content (Tone and Style Reference):** ```markdown --- layout: home --- ![AI generated image](/assets/images/index.png) The Handley Research Group stands at the forefront of cosmological exploration, pioneering novel approaches that fuse fundamental physics with the transformative power of artificial intelligence. We are a dynamic team of researchers, including PhD students, postdoctoral fellows, and project students, based at the University of Cambridge. Our mission is to unravel the mysteries of the Universe, from its earliest moments to its present-day structure and ultimate fate. We tackle fundamental questions in cosmology and astrophysics, with a particular focus on leveraging advanced Bayesian statistical methods and AI to push the frontiers of scientific discovery. Our research spans a wide array of topics, including the [primordial Universe](https://arxiv.org/abs/1907.08524), [inflation](https://arxiv.org/abs/1807.06211), the nature of [dark energy](https://arxiv.org/abs/2503.08658) and [dark matter](https://arxiv.org/abs/2405.17548), [21-cm cosmology](https://arxiv.org/abs/2210.07409), the [Cosmic Microwave Background (CMB)](https://arxiv.org/abs/1807.06209), and [gravitational wave astrophysics](https://arxiv.org/abs/2411.17663). ### Our Research Approach: Innovation at the Intersection of Physics and AI At The Handley Research Group, we develop and apply cutting-edge computational techniques to analyze complex astronomical datasets. Our work is characterized by a deep commitment to principled [Bayesian inference](https://arxiv.org/abs/2205.15570) and the innovative application of [artificial intelligence (AI) and machine learning (ML)](https://arxiv.org/abs/2504.10230). **Key Research Themes:** * **Cosmology:** We investigate the early Universe, including [quantum initial conditions for inflation](https://arxiv.org/abs/2002.07042) and the generation of [primordial power spectra](https://arxiv.org/abs/2112.07547). We explore the enigmatic nature of [dark energy, using methods like non-parametric reconstructions](https://arxiv.org/abs/2503.08658), and search for new insights into [dark matter](https://arxiv.org/abs/2405.17548). A significant portion of our efforts is dedicated to [21-cm cosmology](https://arxiv.org/abs/2104.04336), aiming to detect faint signals from the Cosmic Dawn and the Epoch of Reionization. * **Gravitational Wave Astrophysics:** We develop methods for [analyzing gravitational wave signals](https://arxiv.org/abs/2411.17663), extracting information about extreme astrophysical events and fundamental physics. * **Bayesian Methods & AI for Physical Sciences:** A core component of our research is the development of novel statistical and AI-driven methodologies. This includes advancing [nested sampling techniques](https://arxiv.org/abs/1506.00171) (e.g., [PolyChord](https://arxiv.org/abs/1506.00171), [dynamic nested sampling](https://arxiv.org/abs/1704.03459), and [accelerated nested sampling with $\beta$-flows](https://arxiv.org/abs/2411.17663)), creating powerful [simulation-based inference (SBI) frameworks](https://arxiv.org/abs/2504.10230), and employing [machine learning for tasks such as radiometer calibration](https://arxiv.org/abs/2504.16791), [cosmological emulation](https://arxiv.org/abs/2503.13263), and [mitigating radio frequency interference](https://arxiv.org/abs/2211.15448). We also explore the potential of [foundation models for scientific discovery](https://arxiv.org/abs/2401.00096). **Technical Contributions:** Our group has a strong track record of developing widely-used scientific software. Notable examples include: * [**PolyChord**](https://arxiv.org/abs/1506.00171): A next-generation nested sampling algorithm for Bayesian computation. * [**anesthetic**](https://arxiv.org/abs/1905.04768): A Python package for processing and visualizing nested sampling runs. * [**GLOBALEMU**](https://arxiv.org/abs/2104.04336): An emulator for the sky-averaged 21-cm signal. * [**maxsmooth**](https://arxiv.org/abs/2007.14970): A tool for rapid maximally smooth function fitting. * [**margarine**](https://arxiv.org/abs/2205.12841): For marginal Bayesian statistics using normalizing flows and KDEs. * [**fgivenx**](https://arxiv.org/abs/1908.01711): A package for functional posterior plotting. * [**nestcheck**](https://arxiv.org/abs/1804.06406): Diagnostic tests for nested sampling calculations. ### Impact and Discoveries Our research has led to significant advancements in cosmological data analysis and yielded new insights into the Universe. Key achievements include: * Pioneering the development and application of advanced Bayesian inference tools, such as [PolyChord](https://arxiv.org/abs/1506.00171), which has become a cornerstone for cosmological parameter estimation and model comparison globally. * Making significant contributions to the analysis of major cosmological datasets, including the [Planck mission](https://arxiv.org/abs/1807.06209), providing some of the tightest constraints on cosmological parameters and models of [inflation](https://arxiv.org/abs/1807.06211). * Developing novel AI-driven approaches for astrophysical challenges, such as using [machine learning for radiometer calibration in 21-cm experiments](https://arxiv.org/abs/2504.16791) and [simulation-based inference for extracting cosmological information from galaxy clusters](https://arxiv.org/abs/2504.10230). * Probing the nature of dark energy through innovative [non-parametric reconstructions of its equation of state](https://arxiv.org/abs/2503.08658) from combined datasets. * Advancing our understanding of the early Universe through detailed studies of [21-cm signals from the Cosmic Dawn and Epoch of Reionization](https://arxiv.org/abs/2301.03298), including the development of sophisticated foreground modelling techniques and emulators like [GLOBALEMU](https://arxiv.org/abs/2104.04336). * Developing new statistical methods for quantifying tensions between cosmological datasets ([Quantifying tensions in cosmological parameters: Interpreting the DES evidence ratio](https://arxiv.org/abs/1902.04029)) and for robust Bayesian model selection ([Bayesian model selection without evidences: application to the dark energy equation-of-state](https://arxiv.org/abs/1506.09024)). * Exploring fundamental physics questions such as potential [parity violation in the Large-Scale Structure using machine learning](https://arxiv.org/abs/2410.16030). ### Charting the Future: AI-Powered Cosmological Discovery The Handley Research Group is poised to lead a new era of cosmological analysis, driven by the explosive growth in data from next-generation observatories and transformative advances in artificial intelligence. Our future ambitions are centred on harnessing these capabilities to address the most pressing questions in fundamental physics. **Strategic Research Pillars:** * **Next-Generation Simulation-Based Inference (SBI):** We are developing advanced SBI frameworks to move beyond traditional likelihood-based analyses. This involves creating sophisticated codes for simulating [Cosmic Microwave Background (CMB)](https://arxiv.org/abs/1908.00906) and [Baryon Acoustic Oscillation (BAO)](https://arxiv.org/abs/1607.00270) datasets from surveys like DESI and 4MOST, incorporating realistic astrophysical effects and systematic uncertainties. Our AI initiatives in this area focus on developing and implementing cutting-edge SBI algorithms, particularly [neural ratio estimation (NRE) methods](https://arxiv.org/abs/2407.15478), to enable robust and scalable inference from these complex simulations. * **Probing Fundamental Physics:** Our enhanced analytical toolkit will be deployed to test the standard cosmological model ($\Lambda$CDM) with unprecedented precision and to explore [extensions to Einstein's General Relativity](https://arxiv.org/abs/2006.03581). We aim to constrain a wide range of theoretical models, from modified gravity to the nature of [dark matter](https://arxiv.org/abs/2106.02056) and [dark energy](https://arxiv.org/abs/1701.08165). This includes leveraging data from upcoming [gravitational wave observatories](https://arxiv.org/abs/1803.10210) like LISA, alongside CMB and large-scale structure surveys from facilities such as Euclid and JWST. * **Synergies with Particle Physics:** We will continue to strengthen the connection between cosmology and particle physics by expanding the [GAMBIT framework](https://arxiv.org/abs/2009.03286) to interface with our new SBI tools. This will facilitate joint analyses of cosmological and particle physics data, providing a holistic approach to understanding the Universe's fundamental constituents. * **AI-Driven Theoretical Exploration:** We are pioneering the use of AI, including [large language models and symbolic computation](https://arxiv.org/abs/2401.00096), to automate and accelerate the process of theoretical model building and testing. This innovative approach will allow us to explore a broader landscape of physical theories and derive new constraints from diverse astrophysical datasets, such as those from GAIA. Our overarching goal is to remain at the forefront of scientific discovery by integrating the latest AI advancements into every stage of our research, from theoretical modeling to data analysis and interpretation. We are excited by the prospect of using these powerful new tools to unlock the secrets of the cosmos. Content generated by [gemini-2.5-pro-preview-05-06](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/content/index.txt). Image generated by [imagen-3.0-generate-002](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/images/index.txt). ``` 2. **Paper Metadata:** ```yaml !!python/object/new:feedparser.util.FeedParserDict dictitems: id: http://arxiv.org/abs/2009.03287v3 guidislink: true link: http://arxiv.org/abs/2009.03287v3 updated: '2021-06-06T16:05:55Z' updated_parsed: !!python/object/apply:time.struct_time - !!python/tuple - 2021 - 6 - 6 - 16 - 5 - 55 - 6 - 157 - 0 - tm_zone: null tm_gmtoff: null published: '2020-09-07T17:52:43Z' published_parsed: !!python/object/apply:time.struct_time - !!python/tuple - 2020 - 9 - 7 - 17 - 52 - 43 - 0 - 251 - 0 - tm_zone: null tm_gmtoff: null title: "Strengthening the bound on the mass of the lightest neutrino with\n terrestrial\ \ and cosmological experiments" title_detail: !!python/object/new:feedparser.util.FeedParserDict dictitems: type: text/plain language: null base: '' value: "Strengthening the bound on the mass of the lightest neutrino with\n\ \ terrestrial and cosmological experiments" summary: '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 $N_\mathrm{eff}$.' summary_detail: !!python/object/new:feedparser.util.FeedParserDict dictitems: type: text/plain language: null base: '' value: '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: - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: The GAMBIT Cosmology Workgroup - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: ':' - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: "Patrick St\xF6cker" - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: "Csaba Bal\xE1zs" - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Sanjay Bloor - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Torsten Bringmann - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: "Tom\xE1s E. Gonzalo" - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Will Handley - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Selim Hotinli - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Cullan Howlett - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Felix Kahlhoefer - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Janina J. Renk - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Pat Scott - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Aaron C. Vincent - !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Martin White author_detail: !!python/object/new:feedparser.util.FeedParserDict dictitems: name: Martin White author: Martin White arxiv_doi: 10.1103/PhysRevD.103.123508 links: - !!python/object/new:feedparser.util.FeedParserDict dictitems: title: doi href: http://dx.doi.org/10.1103/PhysRevD.103.123508 rel: related type: text/html - !!python/object/new:feedparser.util.FeedParserDict dictitems: href: http://arxiv.org/abs/2009.03287v3 rel: alternate type: text/html - !!python/object/new:feedparser.util.FeedParserDict dictitems: title: pdf href: http://arxiv.org/pdf/2009.03287v3 rel: related type: application/pdf arxiv_comment: "5 pages, 2 figures + Appendix. Full dataset available at\n https://doi.org/10.5281/zenodo.4005381\ \ (v3: Matches version published in PRD)" arxiv_journal_ref: Phys. Rev. D 103, 123508 (2021) arxiv_primary_category: term: astro-ph.CO scheme: http://arxiv.org/schemas/atom tags: - !!python/object/new:feedparser.util.FeedParserDict dictitems: term: astro-ph.CO scheme: http://arxiv.org/schemas/atom label: null - !!python/object/new:feedparser.util.FeedParserDict dictitems: term: hep-ph scheme: http://arxiv.org/schemas/atom label: null ``` 3. **Paper Source (TeX):** ```tex \documentclass[aps,twocolumn,prd,showpacs,amsmath,amssymb,superscriptaddress,sort&compress,nofootinbib,preprintnumbers]{revtex4-1} \usepackage{graphicx} \usepackage{xspace} \usepackage{bm} \usepackage{tikz} \usepackage[colorlinks=true, citecolor=blue, urlcolor=blue, filecolor=blue]{hyperref} \usepackage{enumitem} \usepackage{afterpage} \bibliographystyle{apsrev4-2-modified} \newcommand{\aachen}{Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, D-52056 Aachen, Germany} \newcommand{\queens}{Department of Physics, Engineering Physics and Astronomy, Queen's University, Kingston ON K7L 3N6, Canada} \newcommand{\imperial}{Department of Physics, Imperial College London, Blackett Laboratory, Prince Consort Road, London SW7 2AZ, UK} \newcommand{\cambridge}{Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, Cambridge, CB3 0HE, UK} \newcommand{\oslo}{Department of Physics, University of Oslo, Box 1048, Blindern, N-0316 Oslo, Norway} \newcommand{\adelaide}{ARC Centre for Dark Matter Particle Physics, Department of Physics, University of Adelaide, Adelaide, SA 5005, Australia} \newcommand{\monash}{School of Physics and Astronomy, Monash University, Melbourne, VIC 3800, Australia} \newcommand{\mcdonald}{Arthur B. McDonald Canadian Astroparticle Physics Research Institute, Kingston ON K7L 3N6, Canada} \newcommand{\okc}{Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Centre, SE-10691 Stockholm, Sweden} \newcommand{\perimeter}{Perimeter Institute for Theoretical Physics, Waterloo ON N2L 2Y5, Canada} \newcommand{\uq}{School of Mathematics and Physics, The University of Queensland, St.\ Lucia, Brisbane, QLD 4072, Australia} \newcommand{\gottingen}{Institut f\"ur Astrophysik, Georg-August Universit\"at G\"ottingen, Friedrich-Hund-Platz~1, 37077 G\"ottingen, Germany} \newcommand{\ioa}{Institute for Astronomy, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK} \newcommand{\kicc}{Kavli Institute for Cosmology, University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK} \newcommand{\caius}{Gonville \& Caius College, Trinity Street, Cambridge, CB2 1TA, UK} \newcommand{\gambit}{\GB} \newcommand{\GB}{\textsf{GAMBIT}\xspace} \newcommand{\cosmobit}{\textsf{CosmoBit}\xspace} \newcommand{\precisionbit}{\textsf{PrecisionBit}\xspace} \newcommand{\neutrinobit}{\textsf{NeutrinoBit}\xspace} \newcommand{\scannerbit}{\textsf{ScannerBit}\xspace} \newcommand{\Planck}{\emph{Planck}\xspace} \newcommand{\nufit}{\textsf{NuFit}\xspace} \newcommand{\lcdm}{$\Lambda$CDM\xspace} \newcommand{\polychord}{\textsf{PolyChord}\xspace} \newcommand{\montepython}{\textsf{MontePython}\xspace} \newcommand{\alterbbn}{\textsf{AlterBBN}\xspace} \newcommand{\class}{\textsf{CLASS}\xspace} \newcommand{\mnuzero}{m_{\nu_0}} \include{jdefs} \begin{document} \title{Strengthening the bound on the mass of the lightest neutrino \\ with terrestrial and cosmological experiments} \author{The GAMBIT Cosmology Workgroup: Patrick St\"ocker} \email{stoecker@physik.rwth-aachen.de} \affiliation{\aachen} \author{Csaba Bal{\'a}zs} \affiliation{\monash} \author{Sanjay Bloor} \affiliation{\uq} \affiliation{\imperial} \author{Torsten Bringmann} \affiliation{\oslo} \author{Tom\'as E. Gonzalo} \affiliation{\monash} \author{Will Handley} \affiliation{\cambridge} \affiliation{\kicc} \affiliation{\caius} \author{Selim Hotinli} \affiliation{\imperial} \author{Cullan Howlett} \email{c.howlett@uq.edu.au} \affiliation{\uq} \author{Felix Kahlhoefer} \affiliation{\aachen} \author{Janina J. Renk} \email{janina.renk@fysik.su.se} \affiliation{\uq} \affiliation{\imperial} \affiliation{\okc} \author{Pat Scott} \email{pat.scott@uq.edu.au} \affiliation{\uq} \affiliation{\imperial} \author{Aaron C. Vincent} \affiliation{\queens} \affiliation{\mcdonald} \affiliation{\perimeter} \author{Martin White} \affiliation{\adelaide} \date{\today} \begin{abstract} %Must be < 600 characters! \noindent 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 $N_\mathrm{eff}$. \end{abstract} %\pacs{} \preprint{TTK-20-28, gambit-physics-2020} \maketitle \section{Introduction} Neutrino masses are arguably the most concrete evidence to date of physics beyond the Standard Model (SM). Measurements of their flavor oscillations at reactor \cite{Gando:2013nba,An:2016srz,Adey:2018zwh,dchooz,Bak:2018ydk}, accelerator \cite{Adamson:2013whj,Adamson:2013ue,t2k,t2k2,sanchez_mayly_2018_1286758,Acero:2019ksn}, solar \cite{Cleveland:1998nv,Kaether:2010ag,Abdurashitov:2009tn,Aharmim:2011vm,Hosaka:2005um,Cravens:2008aa,Abe:2010hy,skiv,Bellini:2011rx,Bellini:2008mr,Bellini:2014uqa} and atmospheric \cite{Aartsen:2014yll,Abe:2017aap} experiments show that at least two of the three SM neutrinos must be massive. While oscillation experiments probe mass-squared differences between eigenstates, the expansion history of the Universe, growth of cosmic structure and the cosmic microwave background (CMB) are sensitive to absolute masses, which determine when a neutrino becomes nonrelativistic; for most cosmological applications, this is expressed in terms of the sum of masses $\sum m_\nu$. Robust and precise inference on the mass of the lightest state can therefore only be obtained by combining the latest results of all these probes self-consistently, including associated uncertainties from each, as well as constraints on other relevant parameters from e.g.\ big bang nucleosynthesis (BBN) and late-time cosmological observables \cite{Wong:2011ip,Lesgourgues:2014zoa,Vagnozzi:2017ovm,Aghanim:2018eyx,Loureiro:2018pdz,Ivanov:2019hqk,Archidiacono:2020dvx}. As no probe has yet directly measured the mass of a single neutrino, the most convenient three-flavor parametrisation is in terms of the mass $\mnuzero$ of the lightest neutrino and two squared mass splittings, $\Delta m_{21}^2 \equiv m_2^2 - m_1^2$ and $\Delta m_{3l}^2 \equiv m_3^2 - m_l^2$. Here 1, 2 and 3 label the mass eigenstates with the largest component of $\nu_e$, $\nu_\mu$ and $\nu_\tau$, respectively. Two mass orderings are presently permitted by the data: the normal ($m_1 < m_2 \ll m_3$; NH) and inverted hierarchies ($m_3 \ll m_1 < m_2$; IH). $\Delta m_{3l}^2$ refers to the splitting between the lightest and heaviest states, i.e.\ $l=1$ for the NH and $l=2$ for the IH. In terms of the splitting parameters, the physical masses are \begin{eqnarray} \mathrm{NH:}\ &(m_1^2,m_2^2,m_3^2) =& \mnuzero^2 + (0, \Delta m_{21}^2, \Delta m_{3l}^2)\\ \mathrm{IH:}\ &(m_3^2,m_1^2,m_2^2) =& \mnuzero^2 + (0, |\Delta m_{3l}^2|-\Delta m_{21}^2, |\Delta m_{3l}^2|).\nonumber \end{eqnarray} In this article, we make use of the new cosmology module \cosmobit \cite{cosmobit} within the beyond-the-SM global fitting package \GB \cite{gambit} in order to perform the most precise and robust combination to date of cosmological and experimental constraints on the mass of the lightest neutrino. We include the most recent CMB likelihoods from \Planck \cite{Aghanim:2019ame}, recent three-flavor neutrino global fit results from \nufit \cite{Esteban:2018azc}, and correlated measurements of the baryon acoustic oscillation (BAO) scale by 6dF \cite{2011MNRAS.416.3017B}, SDSS-MGS \cite{2015MNRAS.449..835R}, BOSS DR12 \cite{Alam:2016hwk}, eBOSS DR14 \cite{Ata:2017dya,Bautista_2018,Blomqvist2019} and DES \cite{Abbott_2018}. We also compute and propagate the primordial helium abundance and number of effective relativistic degrees of freedom $N_\mathrm{eff}$ through all our calculations and likelihoods self-consistently and account for the uncertainty on the lifetime of the neutron. When computing bounds on neutrino masses, we illustrate the impact of different physical assumptions about $N_\mathrm{eff}$ and show the impact of the choice of neutrino mass model on the derived value of the Hubble parameter $H_0$, of particular interest given the present tension between expansion measurements at early and late times \cite{Riess:2019cxk,2019arXiv190704869W,2019ApJ...882...34F}. \section{Methodology} Our likelihoods are based on the latest and most constraining data implemented in \cosmobit \cite{cosmobit}, \neutrinobit \cite{RHN} and \precisionbit \cite{SDPBit}: \begin{itemize}[noitemsep,topsep=0pt] \item[(i)]Neutrino oscillations: Two-dimensional NH and IH $\Delta \chi^2$ tables for $\Delta m_{3l}^2$ and $\Delta m_{21}^2$ from \nufit \textsf{4.1} \cite{Esteban:2018azc}. These come from fits to the data from solar (Homestake chlorine \cite{Cleveland:1998nv}, Gallex/GNO \cite{Kaether:2010ag}, SAGE \cite{Abdurashitov:2009tn}, SNO \cite{Aharmim:2011vm}, four phases of Super-Kamiokande \cite{Hosaka:2005um,Cravens:2008aa,Abe:2010hy,skiv}, two phases of Borexino \cite{Bellini:2011rx,Bellini:2008mr,Bellini:2014uqa}), atmospheric (IceCube/DeepCore \cite{Aartsen:2014yll}, Super-Kamiokande \cite{Abe:2017aap}), reactor (KamLAND \cite{Gando:2013nba}, Double Chooz \cite{dchooz}, Daya Bay \cite{An:2016srz,Adey:2018zwh}, Reno \cite{Bak:2018ydk}), and accelerator experiments (MINOS \cite{Adamson:2013whj,Adamson:2013ue}, T2K \cite{t2k,t2k2}, NO$\nu$A \cite{sanchez_mayly_2018_1286758,Acero:2019ksn}). The other oscillation parameters (mixing angles $\theta_{ij}$ and \textit{CP} phase $\delta_{CP}$) have no bearing on neutrino mass studies and do not enter our analysis. Updates contained in \nufit \textsf{5.0} \cite{Esteban:2020cvm} released when this article was in the final stages of preparation include only small improvements to the likelihoods for $\Delta m_{3l}^2$ and $\Delta m_{21}^2$, so they have minimal impact on the results we show here. \item[(ii)]BBN: Primordial abundances of $^4$He, $Y_\mathrm{p} = 0.245 \pm 0.003$ \cite{Tanabashi:2018oca} and deuterium, ${\rm D/H} = (2.527 \pm 0.030) \times 10^{-5}$ \cite{Cooke:2017cwo}. \item[(iii)]CMB: \Planck 2018 baseline likelihoods consisting of high-$\ell$ and low-$\ell$ temperature and polarization data, plus CMB lensing \cite{Aghanim:2019ame}. \item[(iv)]Supernovae Type Ia (SN Ia): $1048$ SN Ia included in the Pantheon compilation \cite{Scolnic:2017caz}. \item[(v)]BAO scale: Measurements of the transverse comoving distance $D_{M}$ and the Hubble parameter $H(z)$ from the BOSS DR12 anisotropic consensus \cite{Alam:2016hwk}, $D_{M}$ from DES Y1 \cite{Abbott_2018}, and the volume-averaged distance $D_{V}$ from the combined 6dF and MGS galaxy surveys \cite{2011MNRAS.416.3017B, 2015MNRAS.449..835R, Carter_2018} and the eBOSS DR14 lumious red galaxy (LRG) and quasi-stellar objects (QSO) samples \cite{Ata:2017dya, Bautista_2018}. All measurements are relative to $r_{s}$, the radius of the sound horizon at the baryon-drag epoch. \end{itemize} We carefully consider correlations between overlapping samples in the BAO scale measurements. The 6dF+MGS result can be considered independent of the others, as these samples do not overlap in redshift with the others. Similarly, we treat the DES results as independent of all others, as less than $10\%$ of the DES footprint overlaps with BOSS DR12 or eBOSS DR14. The DES sample also consists of very different targets to BOSS and eBOSS, and uses a different methodology (photometric rather than spectroscopic redshifts). However, the BOSS DR12 and eBOSS results are correlated: The eBOSS LRG sample actually contains some of the same galaxies as BOSS DR12, while the eBOSS QSO sample overlaps substantially with the LRGs both on the sky and in redshift. Overall, there are nonzero correlations that should be accounted for between the measurements $(D_{M}/r_{s})^{\mathrm{BOSS}}$, $(Hr_{s})^{\mathrm{BOSS}}$, $(D_{V}/r_{s})^{\mathrm{eBOSS,LRG}}$, and $(D_{V}/r_{s})^{\mathrm{eBOSS,QSO}}$. To do this in a way that accounts for variation with cosmological parameters, we implement a novel method to compute the cross-correlation coefficients using Fisher matrices, following BAO forecasting techniques \cite{Seo_2007,Font_Ribera_2014}. We sum the Fisher information that each sample contributes to the four overlapping measurements listed above, accounting for redshift and sky overlap. Inverting the full Fisher matrix then gives the correlation coefficients. We do this separately for every combination of cosmological parameters in the fit, using the number density of objects, matter power spectrum and growth rate of structure to model the BOSS/eBOSS galaxy power spectra and their covariance matrices as a function of redshift. We split the models into smooth and oscillatory components to obtain the derivatives of the BAO feature in the power spectrum with respect to the distance measurements, and fix the galaxy bias and nonlinear damping of the power spectra to their best-fit values as reported in the original works. The Fisher matrix calculation then uses these all as inputs, integrating over angles and scales in the clustering measurements consistent with the range used in the original measurements. We find a value for the cross-correlation between BOSS DR12 and the eBOSS LRGs comparable to the one reported in Ref.~\cite{Bautista_2018}. The benefits of our technique are that it includes information from all scales included in the measurement and does so self-consistently for each combination of cosmological parameters. More details on the calculation and the computed correlation coefficients can be found in Appendix~\ref{app:BAO}. We compute the BAO scale and SN Ia likelihoods via an interface to \montepython \textsf{3.3.0} \cite{Audren:2012wb,brinckmann2018montepython}; our novel BAO scale correlation treatment will appear in a future release. For computing observable predictions, we use routines in \cosmobit and associated interfaces to \alterbbn \textsf{2.2} (\cite{Arbey:2011nf,Arbey:2018zfh}; for BBN yields) and \class \textsf{2.9.3} (\cite{Blas:2011rf}; for solving the background cosmology and Boltzmann equations). \begin{table}[t] \centering \begin{tabular}{l|l|l} \hline Sector & Parameter & Range \\ \hline $\nu$ masses &$m _{\nu_0}$ & [0, 1.1]\,eV \\ &$\Delta m^{2}_{21}$ & $[6,\ 9] \times 10^{-5}$\,eV$^2$ \\ $\,\,$(NH) &$\Delta m^{2}_{3l}$ & $[2.2,\ 2.8] \times 10^{-3}$\,eV$^2$ \\ $\,\,$(IH) &$\Delta m^{2}_{3l}$ & $[-2.8,\ -2.2] \times 10^{-3}$\,eV$^2$ \\ \hline \lcdm &$H_0 $ & [50, 80]\,km\,s$^{-1}$\,Mpc$^{-1}$ \\ &$\Omega_\mathrm{b} h^2$ & [0.020, 0.024] \\ &$\Omega_\mathrm{cdm} h^2$ & [0.10, 0.15] \\ &$\tau_\mathrm{reionization} $ & [0.004, 0.20] \\ &$\mathrm{ln}\left(10^{10}\,A_s\right) $ & [2.5,\ 3.5] \\ &$n_s $ & [0.90, 1.10] \\ \hline $N_\mathrm{eff}$ &$r_\nu$ & [0.75, 1.15] \\ \hline Nuisance & SN Ia abs.\ magnitude $M$ & [$-$20, $-$18] \\ & Neutron lifetime $\tau_\mathrm{n}$ & [876, 883]\,s\\ & \textit{Planck} likelihood & 21 parameters varied \\ \hline \end{tabular} \caption{Parameters and ranges varied in the main analysis of this article. All parameters are sampled with linear priors. For the nuisance parameters associated with the \textit{Planck} likelihood, we adopt the same prior ranges as done for the Planck baseline analysis \cite{Aghanim:2019ame} and apply the recommended Gaussian priors as additional likelihood contributions.} \label{tab:priors} \end{table} We perform separate fits of the NH and IH, varying $\mnuzero$, $\Delta m_{21}^2$ and $\Delta m_{3l}^2$, the six free parameters of the standard Lambda cold dark matter cosmology (\lcdm; see \cite{cosmobit} for detailed definitions), and $\Delta N_\mathrm{eff}\equiv N_\mathrm{eff} - N_\mathrm{SM}$ with $ N_\mathrm{SM}= 3.045$ \cite{deSalas:2016ztq,Akita:2020szl,Froustey:2020mcq} (\autoref{tab:priors}). For our main analysis, we conservatively adopt a linear prior on $\mnuzero$ between 0 and 1.1\,eV. In Appendix \ref{app:prior}, we show how the limit on $\mnuzero$ strengthens if we change to a logarithmic prior above $\mnuzero=0.0003$\,eV. We adopt linear priors on the \lcdm parameters, as these are sufficiently well constrained by data that their priors are inconsequential. We assume that $N_\mathrm{eff}$ has the same value during BBN and recombination, varying $\Delta N_\mathrm{eff}$ by scanning linearly over the effective neutrino temperature ratio $r_{\nu,\mathrm{eff}} \equiv T_\nu / T_{\nu,\text{SM}}= (\Delta N_\mathrm{eff}/N_\mathrm{SM} + 1)^\frac14$. This approach enables us to explore the full range of the number of effective relativistic degrees of freedom in the early Universe, corresponding to both positive and negative values of $\Delta N_\mathrm{eff}$. We later explore the impact of restricting our analysis to $\Delta N_\mathrm{eff} \ge 0$, in which case, $\Delta N_\mathrm{eff}$ can be interpreted as the contribution of additional ultrarelativistic (radiation) species and to the pure SM case ($\Delta N_\mathrm{eff} = 0$). Finally, we vary a total of 23 nuisance parameters representing uncertainties in the SN Ia absolute magnitude, the \textit{Planck} analysis, and the neutron lifetime. These nuisance parameters are constrained, respectively, with the \montepython likelihood for the magnitude of Pantheon supernovae, a likelihood implementation of the \textit{Planck} nuisance priors \cite{Aghanim:2019ame}, and the combination of all ``bottle'' measurements of the lifetime of the neutron $\tau_{n\,,\text{bottle}} = 879.4 \pm 0.6$\,s \cite{PDG20}. We employ the nested sampler \polychord \textsf{1.17.1} \cite{Handley:2015} in fast-slow mode via \scannerbit \cite{scannerbit} in order to oversample \textit{Planck} and SN Ia nuisances. Our fits use 500 live points, 5000 initial samples from the prior, a stopping tolerance of 0.01, $n_\mathrm{repeats}=2n_\mathrm{slow}=22$, a 1:3 fast-slow timing split (leading to approximately 340 likelihood evaluations with different nuisance parameters per combination of the remaining parameters), and default values for all other settings. \section{Results} Assuming \lcdm cosmology plus a free $N_\mathrm{eff}$ and normal mass ordering, we find a global 95\% confidence upper bound on the lightest neutrino mass of $\mnuzero < 0.037$\,eV; for inverted ordering, this increases slightly to $\mnuzero < 0.042$\,eV. In terms of the sum of neutrino masses, this corresponds to $0.058 < \sum m_\nu / \mathrm{eV} < 0.139$ (NH) and $0.098 < \sum m_\nu / \mathrm{eV} < 0.174$ (IH). \begin{figure}[t] \centering \includegraphics[width=\columnwidth,clip,trim=5 8 5 0]{figures/fig1_triangle_alt2_PC500} \caption{1D and joint 2D posteriors (bottom left) and profile likelihoods (upper right) on the lightest neutrino mass, the sum of neutrino masses, the number of effective neutrino species at the time of CMB formation, and the Hubble parameter, based on the most robust and complete combination to date of CMB, BAO scale, SN Ia, BBN and neutrino oscillation data. Posteriors are shown for normal and inverted neutrino hierarchies and are compared with the often-seen (but unphysical) scenario of three degenerate-mass neutrinos. Profile likelihoods are for the normal hierarchy only and assume the best-fit values from the corresponding posterior scan for the 21 \textit{Planck} nuisance parameters. Shading indicates 68\% and 95\% credible/confidence regions. \label{fig1}} \end{figure} The lower-left triangle of \autoref{fig1} compares the one- and two-dimensional marginalized posterior distributions for the normal and inverted hierarchies. Here we show both the lightest neutrino mass and the sum of neutrino masses, as well as their correlations with $N_\mathrm{eff}$ and $H_0$. We also show the result for the canonical scenario considered in most previous analyses, such as those by both \textit{Planck} \cite{Aghanim:2018eyx} and eBOSS \cite{Alam:2020sor}, where a single parameter specifies a common degenerate mass for all three neutrinos. In all cases, the maximum posterior probability density is achieved for a massless lightest neutrino, reflecting the fact that there remains no positive cosmological hint for neutrino mass to date. The degenerate-mass assumption would lead one to erroneously infer that $\sum m_\nu / \mathrm{eV} < 0.115$ at 95\% confidence. This result is plainly biased toward lower values due to the fact that the majority of the probability distribution lies within the unphysical region excluded by neutrino oscillation experiments. Using a physically realistic mass model shifts the 95\% interval for $H_0$ from $67.7\pm 1.7$\,km\,s$^{-1}$\,Mpc$^{-1}$ to $67.5\pm 1.8$\,km\,s$^{-1}$\,Mpc$^{-1}$ (NH) or $67.4\pm 1.7$\,km\,s$^{-1}$\,Mpc$^{-1}$ (IH), and the 95\% interval for $N_\mathrm{eff}$ from $3.04\pm 0.24$ to $3.06\pm 0.24$ (NH) or $3.08\pm 0.24$ (IH). For comparison, in the upper-right triangle of \autoref{fig1}, we also show prior-independent profile likelihoods for the NH obtained from the differential evolution sampler \textsf{Diver} \cite{scannerbit} with a population of $10^4$, a convergence threshold of $10^{-4}$, and the \textit{Planck} nuisance parameters fixed to their best-fit values from the NH \polychord fit (as \textsf{Diver} has no fast-slow feature). The results match the posteriors reasonably closely, but give slightly stronger implied constraints at 95\% confidence: $\mnuzero < 0.033$\,eV and $0.058 < \sum m_\nu / \mathrm{eV} < 0.127$.\footnote{The slightly higher profile likelihood than posterior for much of the allowed range of $\sum m_\nu$ should be understood in the context of frequentist confidence levels deriving from isolikelihood contours, rather than integrated posterior probabilities as in the case of Bayesian credible regions.} These findings confirm the robustness of our main (Bayesian) results. We have also calculated Bayesian evidences and find that the IH is disfavored relative to the NH with Bayes factors between $\log B = 5.6$ and $\log B = 7.0$ (depending on the treatment of $N_\text{eff}$), a result driven mostly by the neutrino oscillation likelihoods~\cite{deSalas:2020pgw}. \begin{figure}[t] \centering \includegraphics[width=0.95\columnwidth]{figures/fig2_PC500} \caption{Comparison of posterior probabilities for the mass of the lightest neutrino under three different assumptions: $\Delta N_\mathrm{eff} = 0$, $\Delta N_\mathrm{eff} \ge 0$ corresponding to dark radiation, or $\Delta N_\mathrm{eff}$ free to take on positive or negative values, corresponding to a modified effective neutrino temperature.} \label{fig2} \end{figure} In \autoref{fig2}, we examine the impacts of different physical sources of $N_\mathrm{eff}$: (a) changes in the neutrino temperature, where $\Delta N_\mathrm{eff}$ is allowed to be positive or negative, as in our benchmark analyses, (b) dark radiation, where $\Delta N_\mathrm{eff}\ge0$, and (c) the pure SM case, where $\Delta N_\mathrm{eff}=0$. The resulting posteriors only change very slightly, corresponding to shifts of the order of 0.002--0.003\,eV in the 95\% limit on $\mnuzero$. Our final results can therefore be considered rather robust to assumptions about $\Delta N_\mathrm{eff}$. \autoref{fig2} suggests that at the 68\% confidence level, allowing positive $\Delta N_\mathrm{eff}$ may weaken the limits slightly compared to $\Delta N_\mathrm{eff} = 0$, with the effect offset to some extent by also allowing $\Delta N_\mathrm{eff} < 0$. Any such effect is however small enough that it is difficult to distinguish from sampling noise. Notably, bounds on $\mnuzero$ and $\sum m_\nu$ can be weakened substantially in cosmologies featuring \textit{both} dark radiation and a modified neutrino temperature \cite{cosmobit}, neutrino self-interactions, or exotic dark energy, even to the level where a direct measurement of the neutrino mass may be within reach of the KATRIN experiment~\cite{Aker:2019uuj}. \section{Discussion} Our analysis provides a more precise and robust limit on the sum of neutrino masses than either those of \textit{Planck} \cite{Aghanim:2018eyx} or eBOSS \cite{Alam:2020sor}, mainly due to our use of physical neutrino mass models rather than the assumption of degenerate masses. Comparing results for the unphysical degenerate-mass model however provides an indication of the constraining power of the cosmological data used in each case. Our limit ($\sum m_\nu / \mathrm{eV} < 0.115$) is very close to the most similar combination in Ref.\ \cite{Aghanim:2018eyx} ($\sum m_\nu / \mathrm{eV} < 0.12$, \textit{Planck} TT,TE,EE+lowE+lensing+BAO, with varying $N_{\rm{eff}}$), indicating that within $\Lambda$CDM+$N_\text{eff}$ the eBOSS DR14 and DES BAO and Pantheon SN Ia measurements only add limited additional information. The most similar eBOSS limit ($\sum m_\nu / \mathrm{eV} < 0.099$) is stronger. Reference \cite{Alam:2020sor} includes slightly more up-to-date eBOSS BAO scale measurements compared to our analysis, but the improved sensitivity is mainly driven by their inclusion of redshift-space distortions (RSD). We do not include RSD measurements, as to date they have been based on templates for the matter power spectrum that assume a particular neutrino mass, and the fits then neglect the scale dependence in the growth rate of structure. As such we believe they cannot robustly be used to constrain neutrino masses. Reference \cite{Alam:2020sor} also includes new (DR16) Ly$\alpha$ constraints on the BAO scale. We checked that including DR14 Ly$\alpha$ measurements has no impact on our limit. Given this result, the fact that the redshifts probed by Ly$\alpha$ data are intermediate between those of the CMB and other BAO measurements, that Ly$\alpha$ BAO are slightly discrepant with other BAO, and that the Ly$\alpha$ BAO results require more precise control over observational and astrophysical systematics than galaxy BAO \cite{Blomqvist2019}, we argue that excluding the DR14 Ly$\alpha$ result gives a more robust limit on neutrino masses at no decrease in the statistical constraining power. The limits that we present here on the mass of the lightest neutrino are almost 60\% stronger than those derived from a combined fit to both mass hierarchies in a recent similar analysis ($\mnuzero < 0.086$\,eV \cite{Loureiro:2018pdz}), and 14\% stronger than those appearing in a similar contemporaneous analysis \cite{deSalas:2020pgw}. At the limiting value of $\mnuzero$, this brings the absolute scale of neutrino masses down to a level comparable to the larger of the two mass splittings ($m_3 - m_1=0.025$\,eV in the NH, $m_2 - m_3=0.023$\,eV in the IH). We use the same BBN and SN~Ia data as Ref.\ \cite{Loureiro:2018pdz} but improved neutrino and CMB data: results from \nufit \textsf{4.1} rather than \textsf{2.1} for neutrino experiments (leading to roughly 20\% stronger bounds), and a CMB likelihood based on 2018 rather than 2015 \textit{Planck} data (leading to roughly 30\% stronger bounds). Compared to \cite{deSalas:2020pgw}, we add BBN constraints, DES, and eBOSS BAO scale data and marginalize over $N_\mathrm{eff}$. We also propagate the primordial helium abundance fully and incorporate the uncertainty on the lifetime of the neutron (see also discussion in Ref.\ \cite{cosmobit}). From galaxy surveys, we and Ref.\ \cite{deSalas:2020pgw} rely exclusively on scale measurements, as a correct statistical combination of scale data can provide a strong limit on neutrino masses that is also very robust. Reference \cite{Loureiro:2018pdz} instead used an angular clustering reanalysis of the BOSS DR12 data. Their approach used the full shape of the clustering more self-consistently than template-based RSD measurements but still required several uncertainties such as the galaxy bias, redshift error dispersions, and spectroscopic redshift errors to be modeled, and data cuts to be made, adding 28 more nuisance parameters. In principle, nonlinear scales should provide the most constraining power on neutrino mass parameters but difficulty in the modeling limits the accessibility of this information \cite{Font-Ribera:2013wce}. With current analysis techniques, BAO scale measurements still add more constraining power for neutrino masses than data encoding the full shape of the galaxy power spectrum---although this is not expected to remain true for much longer \cite{Ivanov:2019hqk}. \section{Summary} We have presented a comprehensive combined analysis of recent neutrino oscillation, CMB, SN Ia, BBN, and BAO scale data deriving the most accurate and precise limits to date on the mass of the lightest neutrino and the sum of neutrino masses. Assuming normal mass ordering and standard cosmology plus $\Delta N_\mathrm{eff}\ne0$, we have found $\mnuzero < 0.037$\,eV and $0.058 < \sum m_\nu / \mathrm{eV} < 0.139$. With inverted ordering, $\mnuzero < 0.042$\,eV and $0.098 < \sum m_\nu / \mathrm{eV} < 0.174$. These results should serve as a benchmark in the coming years, as neutrino cosmology continues its inexorable progress toward a measurement of the absolute neutrino mass scale. All input files and parameter samples produced for this article can be found on \textsf{Zenodo} \cite{CosmoBit_numass_zenodo}. \section*{Acknowledgements} We thank the \gambit Community, Alex Arbey, Thejs Brinckmann, Tamara Davis, Martina Gerbino, Deanna Hooper, Julien Lesgourgues, Vivian Poulin, Nils Sch\"{o}neberg, Jes\'{u}s Torrado and Sunny Vagnozzi for helpful discussions, PRACE for access to Joliot-Curie at CEA, RWTH Aachen University for access to JARA under Project No. jara0184 and the University of Cambridge for access to CSD3 resources. P.~St. and F.~K. acknowledge funding from Deutsche Forschungsgemeinschaft Grant No.~KA~4662/1-1, C.~B., T.~E.~G., M.~J.~W., P.~Sc. and C.~H. from Australian Research Cuncil Grants No.~DP180102209, No.~FL180100168, No.~CE200100008, and No.~FT190100814, J.~J.~R. from Swedish Research Council Contract No.~638-2013-8993, W.~H. from a Gonville \& Caius Research Fellowship and the George Southgate visiting fellowship, and A.~C.~V. from the Arthur B. McDonald Canadian Astroparticle Physics Research Institute, Canada Foundation for Innovation and Ontario Ministry of Economic Development, Job Creation and Trade (MEDJCT). Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science, and Economic Development, and by the Province of Ontario through MEDJCT. This article made use of \textsf{matplotlib}~\cite{Hunter:2007}, \textsf{GetDist}~\cite{Lewis:2019xzd}, and \textsf{pippi}~\cite{pippi}. \appendix \section{Details of BAO scale correlation coefficients} \label{app:BAO} Here we provide more detail on our novel method to account for the correlations between overlapping BAO experiments in a cosmology-dependent way. We acknowledge that the use of cosmology-dependent Gaussian covariance matrices can lead to an overestimation of the Fisher information \citep{Carron_2013}; however, in our method we are only computing the cross-correlation coefficients, which are then scaled by the original measurement errors. We do not modify these original errors and so are not underestimating the uncertainty. More so, we argue that including cosmology dependence in the correlation coefficients is the correct thing to do, as the overlap between BAO measurements is mainly related to the (effective) cosmological volume shared by the experiments, which is clearly a function of the cosmological model. We begin by expressing the joint covariance matrix of BAO measurements from the overlapping BOSS DR12 and eBOSS results $\boldsymbol{\mathsf{C}}$ in terms of the inverse of the Fisher matrix $\boldsymbol{\mathsf{F}}$, \begin{equation} \boldsymbol{\mathsf{F}}^{-1} = \boldsymbol{\mathsf{C}} = \boldsymbol{\mathsf{E}} \begin{pmatrix} 1 & \rho^\mathrm{BOSS}_{D_{M}/r_{s},Hr_{s}} & c_{0} & 0 \\ \rho^\mathrm{BOSS}_{D_{M}/r_{s},Hr_{s}} & 1 & c_{1} & 0 \\ c_{0} & c_{1} & 1 & c_{2} \\ 0 & 0 & c_{2} & 1 \\ \end{pmatrix} \boldsymbol{\mathsf{E}}. \end{equation} Here, $c_0$ is the correlation coefficient between measurements $(D_{M}/r_{s})^{\mathrm{BOSS}}$ and $(D_{V}/r_{s})^{\mathrm{eBOSS,LRG}}$, $c_1$ is the correlation between $(Hr_{s})^{\mathrm{BOSS}}$ and $(D_{V}/r_{s})^{\mathrm{eBOSS,LRG}}$, and $c_2$ is the correlation between $(D_{V}/r_{s})^{\mathrm{eBOSS,LRG}}$ and $(D_{V}/r_{s})^{\mathrm{eBOSS,QSO}}$. The cross-correlation $\rho^{BOSS}_{D_{M}/r_{s},Hr_{s}}$ between the BOSS DR12 measurements of $D_{M}/r_{s}$ and $Hr_{s}$ is provided as part of the BOSS DR12 results in \montepython and is not replaced in this analysis, or made dependent upon cosmological parameters. The matrix $\boldsymbol{\mathsf{E}}=\mathrm{diag}(\sigma^\mathrm{BOSS}_{D_{M}/r_{s}}, \sigma^\mathrm{BOSS}_{Hr_{s}}, \sigma^\mathrm{eBOSS,LRG}_{D_{V}/r_{s}}, \sigma^\mathrm{eBOSS,QSO}_{D_{V}/r_{s}})$ contains the experimental uncertainties from the BAO measurements, which are also included in \montepython. Hence the only unknowns are $c_{i}$, which we calculate for each set of cosmological parameters by inverting the full Fisher matrix. In practice, we compute the Fisher matrix for the BAO scale parameters \begin{equation} \alpha=\frac{D_{V}r^{\mathrm{fid}}_{s}}{D^{\mathrm{fid}}_{V}r_{s}}, \quad \alpha_{\perp}=\frac{D_{M}r^{\mathrm{fid}}_{s}}{D^{\mathrm{fid}}_{M}r_{s}}, \quad \alpha_{||}=\frac{H^{\mathrm{fid}}r^{\mathrm{fid}}_{s}}{Hr_{s}}, \end{equation} where ``fid'' corresponds to the fiducial cosmology used to make the original clustering measurements. It is trivial to convert the correlation coefficients to those for the distance scales that we actually fit in \montepython. We do this based on \cite{Howlett_2016}, writing the Fisher matrix elements for each parameter of interest as a sum over the information from the different redshift bins and overlapping/nonoverlapping sky areas for each survey. For example, consider the redshift range $0.60 < z < 0.75$. For each redshift bin in this range, we have information contributing to three parameters: $\alpha^{\mathrm{BOSS}}_{\perp}$, $\alpha_{||}^{\mathrm{BOSS}}$ and $\alpha^{\mathrm{eBOSS,LRG}}$. We first compute the $2 \times 2$ Fisher ``submatrix'' for $\alpha^{\mathrm{BOSS}}_{\perp}$, $\alpha_{||}^{\mathrm{BOSS}}$ from the nonoverlapping sky area $\Omega^{\mathrm{BOSS}}-\Omega^{\mathrm{eBOSS,LRG}}$ and add this to the full matrix, then add on the $3 \times 3$ Fisher submatrix for all three parameters from the sky area $\Omega^{\mathrm{eBOSS,LRG}}$. %In this way we build up a complete matrix for all correlated parameters. The Fisher matrix element for parameters $\lambda_{i}$ and $\lambda_{j}$ measured from survey $A$ within a redshift bin is \cite{Tegmark_1997} \begin{equation} F^{A}_{ij} = \int_{0}^{k_{\mathrm{max}}} k^{2} dk \int_{0}^{1} d\mu \frac{\partial P^{A}_{g}(k,\mu)}{\partial \lambda_{i}} C^{-1}_{P^{A}_{g}}(k,\mu) \frac{\partial P^{A}_{g}(k,\mu)}{\partial \lambda_{j}}, \label{eq:fisher} \end{equation} where we fix $k_{\mathrm{max}}=0.3h\,\mathrm{Mpc^{-1}}$. $C_{P^{A}_{g}}(k,\mu)$ is the covariance matrix of the galaxy power spectrum $P^{A}_{g}(k,\mu)$, \begin{equation} C_{P^{A}_{g}}(k,\mu) = \frac{4\pi^{2}}{V^{A}}\biggl[P^{A}_{g}(k,\mu)+\frac{V^{A}}{N^{A}}\biggl]^{2}, \end{equation} where $N^{A}$ is the number of galaxies in the redshift bin, and $V^{A}$ is the cosmological volume contained within the redshift bin and sky area $\Omega^{A}$. The first term in the covariance matrix models cosmic variance; the second is shot noise from the finite number of galaxies. We model the galaxy power spectrum as a function of the matter power spectrum $P_{m}(k)$ and potentially scale-dependent growth rate of structure $f(k)$, splitting it into two components using the smoothed matter power spectrum $P_{sm}(k)$, \begin{multline} P^{A}_{g}(k,\mu) = (b^{A}+f(k)\mu^{2})^{2}P_{sm}(k) \\ \times \biggl[1+\biggl(\frac{P_{m}(k)}{P_{sm}(k)}-1\biggl)e^{-\frac{1}{2}k^{2}[\mu^{2}\Sigma^{A}_{nl,||} + (1 - \mu^{2})\Sigma^{A}_{nl,\perp}]}\biggl]. \end{multline} Here $b^{A}$ represents the linear galaxy bias for the survey, and $\Sigma^{A}_{nl,||}$ and $\Sigma^{A}_{nl,\perp}$ account for nonlinear damping of the BAO feature. The values for these are fixed to the best-fit values from the BOSS and eBOSS analyses. We compute $P_{sm}(k)$ using the method of Ref.\ \cite{Hinton_2016}. \begin{figure}[t] \centering \includegraphics[width=.975\columnwidth]{figures/fig3_triangle_rectangle_PC500} \caption{1D and joint 2D posteriors for the correlation coefficients $c_0$ [$(D_{M}/r_{s})^{\mathrm{BOSS}}$ and $(D_{V}/r_{s})^{\mathrm{eBOSS,LRG}}$], $c_1$ [$(Hr_{s})^{\mathrm{BOSS}}$ and $(D_{V}/r_{s})^{\mathrm{eBOSS,LRG}}$], and $c_2$ [$(D_{V}/r_{s})^{\mathrm{eBOSS,LRG}}$ and $(D_{V}/r_{s})^{\mathrm{eBOSS,QSO}}$]. Also shown are the variations of the correlation coefficients with neutrino mass parameters $N_\mathrm{eff}$ and the Hubble parameter $H_0$. \label{fig3}} \end{figure} The split into smooth and nonsmooth components of the matter power spectrum ensures that we are only including information from the BAO scale, and not the broadband shape of the power spectrum or redshift-space distortions. As such, the derivatives with respect to $\lambda_{i,j}$ in Eq.~(\ref{eq:fisher}) are computed only on the $P_{m}(k)/P_{sm}(k)$ component of $P^{A}_{g}(k,\mu)$. We do this by finite differencing $P_{m}(k')/P_{sm}(k')$ evaluated at $k'=k/\alpha$ or \begin{equation} k' = \frac{k}{\alpha_{\perp}}\biggl[1 + \mu^{2}\biggl(\frac{\alpha^{2}_{\perp}}{\alpha^{2}_{||}}-1\biggl)\biggl]^{1/2}. \end{equation} Overall, the calculation of the Fisher matrix for a particular redshift bin and survey matches that commonly used in the literature \cite{Seo_2007,Font_Ribera_2014} and our model power spectrum is representative of how BAO constraints are actually extracted from the data \cite{Alam:2016hwk,Ata:2017dya}. In \autoref{fig3}, we show the distribution of the correlation coefficients in our BAO scale joint likelihood from our main NH fit. The variation of the correlation coefficients with cosmological parameters is small but perceptible, with $c_1$ and $c_2$ both increasing along with $H_0$ and $N_\mathrm{eff}$, and $c_0$ decreasing with larger $H_0$ and $N_\mathrm{eff}$. The trends are weaker but in the opposite direction for the neutrino mass parameters. In general $c_1$ and $c_2$ are strongly correlated with each other and anticorrelated with $c_0$. Our method can be easily extended to include other datasets, and we expect larger variation in the values of the coefficients for models including nonzero curvature or non-cosmological-constant models of dark energy. \section{Impacts of priors on the mass of the lightest neutrino} \label{app:prior} \begin{figure}[b] \centering \includegraphics[width=\columnwidth]{figures/fig4_triangle_PC500} \caption{1D and joint 2D posteriors on the neutrino mass and relevant cosmological parameters, assuming normal ordering. Here we reproduce the results from \autoref{fig1} based on a linear prior for the mass of the lightest neutrino and compare them to the results when employing a hybrid prior, linear below $\mnuzero=0.0003$\,eV and logarithmic above.} \label{fig4} \end{figure} In the main body of this article, we presented only results based on a linear prior for the lightest neutrino mass $\mnuzero$. This is a conservative choice, as it is an essentially uninformative prior (but see Ref.\ \cite{Heavens:2018adv} for an objective Bayesian construction of the most uninformative prior for this problem). Although more informative, a logarithmic prior is arguably more physically justified: Given that we have no information suggesting any preferred scale for $\mnuzero$ (or, in fact any preference for $\mnuzero>0$ at all), one might argue that any scale for the mass is as likely as another. In \autoref{fig4} we compare our result for the NH with the result if we instead adopt a logarithmic prior for $\mnuzero$ above $0.0003$\,eV (and retain the linear prior below this value, enforcing continuity of the prior across the transition). Masses below 0.0003\,eV are indistinguishable from the massless case in the outputs of \class, so there is little point in oversampling this region. As can be seen from \autoref{fig4}, this hybrid linear-logarithmic prior indeed results in a much stronger preference for very small neutrino masses, giving $\mnuzero < 0.020$\,eV and $0.058 < \sum m_\nu / \mathrm{eV} < 0.100$ at 95\% confidence. The effect is similar in the IH, producing $\mnuzero < 0.024$\,eV and $0.098 < \sum m_\nu / \mathrm{eV} < 0.136$ at 95\% confidence. \vspace{4cm} \bibliography{R2} \end{document} % Bibliography and bibfile \def\ppnp{Prog.\ Part.\ Nuc.\ Phys.} % Progress in Particle and Nuclear Physics \def\pdu{Phys.\ Dark Univ.} % Physics of the Dark Universe \def\astropacific{Astron.\ Soc.\ Pacific Conf.\ Ser.} % Astronomical Society of the Pacific Conference Series \def\lnp{Lec.\ Notes in Physics} % Lecture Notes in Physics \def\cpc{Comp.\ Phys.\ Comm.} % Computer Physics Communications \def\jpg{J. Phys. G} % Journal of Physics G Nuclear Physics \def\ijmpa{Int.\ J.\ Mod.\ Phys.\ A} % International Journal of Modern Physics A \def\ijmpd{Int.\ J.\ Mod.\ Phys.\ D} % International Journal of Modern Physics D \def\epjc{Eur.\ Phys.\ J.\ C} % European Physical Journal C \def\nima{Nuc.\ Inst.\ Methods A} % Nuclear Instruments and Methods A \def\nimb{Nuc.\ Inst.\ Methods B} % Nuclear Instruments and Methods B \def\njp{New J.\ Phys.} % New Journal of Physics \def\rmp{Rev.\ Mod.\ Phys.} % Reviews of Modern Physics \def\app{Astropart.\ Phys.} % Astroparticle Physics \def\aj{AJ}% % Astronomical Journal \def\actaa{Acta Astron.}% % Acta Astronomica \def\araa{ARA\&A}% % Annual Review of Astron and Astrophys \def\arnps{Ann.~Rev.~Nucl.~\& Part.~Sci.}% % Annual Review of Astron and Astrophys \def\apj{ApJ}% % Astrophysical Journal \def\apjl{ApJ}% % Astrophysical Journal, Letters \def\apjs{ApJS}% % Astrophysical Journal, Supplement \def\ao{Appl.\ Opt.}% % Applied Optics \def\apss{Ap\&SS}% % Astrophysics and Space Science \def\aap{A\&A}% % Astronomy and Astrophysics \def\aapr{A\&A~Rev.}% % Astronomy and Astrophysics Reviews \def\aaps{A\&AS}% % Astronomy and Astrophysics, Supplement \def\azh{AZh}% % Astronomicheskii Zhurnal \def\pos{PoS}% % Proceedings of Science \def\baas{BAAS}% % Bulletin of the AAS \def\bac{Bull.\ Astr.\ Inst.\ Czechosl.}% % Bulletin of the Astronomical Institutes of Czechoslovakia \def\caa{Chinese Astron.\ Astrophys.}% % Chinese Astronomy and Astrophysics \def\cjaa{Chinese J.\ Astron.\ Astrophys.}% % Chinese Journal of Astronomy and Astrophysics \def\icarus{Icarus}% % Icarus \def\jhep{JHEP}% % Journal of High Energy Physics \def\jcap{JCAP}% % Journal of Cosmology and Astroparticle Physics \def\jpsj{J.\ Phys.\ Soc.\ Japan}% % Journal of the Physical Society of Japan \def\jrasc{JRASC}% % Journal of the RAS of Canada \def\canjphys{Can.~J.~Phys.} %Canadian Journal of Physics \def\apphys{Astropart.~Phys.} %Astroparticle Physics \def\mnras{MNRAS}% % Monthly Notices of the RAS \def\memras{MmRAS}% % Memoirs of the RAS \def\na{New A}% % New Astronomy \def\nar{New A Rev.}% % New Astronomy Review \def\pasa{PASA}% % Publications of the Astron. Soc. of Australia \def\pra{Phys.\ Rev.\ A}% % Physical Review A: General Physics \def\prb{Phys.\ Rev.\ B}% % Physical Review B: Solid State \def\prc{Phys.\ Rev.\ C}% % Physical Review C \def\prd{Phys.\ Rev.\ D}% % Physical Review D \def\pre{Phys.\ Rev.\ E}% % Physical Review E \def\prl{Phys.\ Rev.\ Lett.}% % Physical Review Letters \def\pasp{PASP}% % Publications of the ASP \def\pasj{PASJ}% % Publications of the ASJ \def\qjras{QJRAS}% % Quarterly Journal of the RAS \def\rmxaa{Rev. Mexicana Astron. Astrofis.}% % Revista Mexicana de Astronomia y Astrofisica \def\skytel{S\&T}% % Sky and Telescope \def\solphys{Sol.\ Phys.}% % Solar Physics \def\sovast{Soviet~Ast.}% % Soviet Astronomy \def\ssr{Space~Sci.\ Rev.}% % Space Science Reviews \def\zap{ZAp}% % Zeitschrift fuer Astrophysik \def\nat{Nature}% % Nature \def\science{Science}% \def\sci{\science}% % Science \def\iaucirc{IAU~Circ.}% % IAU Cirulars \def\aplett{Astrophys.\ Lett.}% % Astrophysics Letters \def\apspr{Astrophys.\ Space~Phys.\ Res.}% % Astrophysics Space Physics Research \def\bain{Bull.\ Astron.\ Inst.\ Netherlands}% % Bulletin Astronomical Institute of the Netherlands \def\fcp{Fund.\ Cosmic~Phys.}% % Fundamental Cosmic Physics \def\gca{Geochim.\ Cosmochim.\ Acta}% % Geochimica Cosmochimica Acta \def\grl{Geophys.\ Res.\ Lett.}% % Geophysics Research Letters \def\jcp{J.\ Chem.\ Phys.}% % Journal of Chemical Physics \def\jgr{J.\ Geophys.\ Res.}% % Journal of Geophysics Research \def\jqsrt{J.\ Quant.\ Spec.\ Radiat.\ Transf.}% % Journal of Quantitiative Spectroscopy and Radiative Trasfer \def\memsai{Mem.\ Soc.\ Astron.\ Italiana}% % Mem. Societa Astronomica Italiana \def\nphysa{Nucl.\ Phys.\ A}% % Nuclear Physics A \def\nphysb{Nucl.\ Phys.\ B}% % Nuclear Physics B \def\physrep{Phys.\ Rep.}% % Physics Reports \def\physscr{Phys.\ Scr}% % Physica Scripta \def\planss{Planet.\ Space~Sci.}% % Planetary Space Science \def\procspie{Proc.\ SPIE}% % Proceedings of the SPIE \def\repprogphys{Rep.\ Prog.\ Phys.}% % Reports of Progress in Physics \def\jpcrd{J. Phys. Chem. Ref. Data}% %Journal of Physical and Chemical Reference Data \def\jphysb{J. Phys. B}% %Journal of Physics B Atomic Molecular Physics \def\jphysd{J. Phys. D}% %Journal of Physics D \def\jphysconfseries{J. Phys. Conf. Series}% %Journal of Physics: Conference Series \def\physrev{\pr} \def\pr{Phys. Rev.}% %Physical Review \def\josa{J. Opt. Soc. Amer. (1917-1983)}% %Journal of the Optical Society of America (1917-1983) \def\josab{J. Opt. Soc. Amer. B}% %Journal of the Optical Society of America B Optical Physics \def\pla{Phys. Lett. A}% %Physics Letters A \def\plb{Phys. Lett. B}% %Physics Letters B \def\os{Opt. Spectrosc. (Russ.)}% %Optics and Spectroscopy (Russ. / USSR) \def\jas{J. Appl. Spectrosc.}% %Journal of Applied Spectroscopy (Russ. / USSR) \def\annp{Ann. Phys.}% %Annalen der Physik \def\sa{Spectrochim. Acta}% %Spectrochimica Acta \def\prsoca{Proc. R. Soc. London Ser. A}% %Proceedings of the Royal Society of London, Series A \def\zphysa{Z. Phys. A}% %Zeitschrift fur Physik A \def\zphysb{Z. Phys. B}% %Zeitschrift fur Physik B \def\zphysc{Z. Phys. C}% %Zeitschrift fur Physik C \def\zphysd{Z. Phys. D}% %Zeitschrift fur Physik D \def\zphyse{Z. Phys. E}% %Zeitschrift fur Physik E \def\zphys{Z. Phys.}% %Zeitschrift fur Physik \def\adndt{Atom. Data Nuc. Data Tables}% %Atomic Data and Nuclear Data Tables \def\jmolspec{J. Mol. Spectrosc.}% %Journal of Molecular Spectroscopy \def\aphysb{Appl. Phys. B}% %Applied Physics B: Lasers and Optics \def\nim{Nuc. Inst. 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(Paris)}% %Journal de Physique \def\epjp{Eur.~Phys.~J.~Plus}% %European Physical Journal Plus \def\epjc{Eur.~Phys.~J.~C}% %European Physical Journal C \def\epl{Europhys.~Lett}% %Europhysics Letters \def\njp{New J.~Phys.} %New Journal of Physics \def\pdu{Phys.~Dark.~Univ.} %Physics of the Dark Universe \let\astap=\aap \let\apjlett=\apjl \let\apjsupp=\apjs \let\applopt=\ao % ``` 4. **Bibliographic Information:** ```bbl %apsrev4-2.bst 2019-01-14 (MD) hand-edited version of apsrev4-1.bst %Control: key (0) %Control: author (72) initials jnrlst %Control: editor formatted (1) identically to author %Control: production of article title (-1) disabled %Control: page (0) single %Control: year (1) truncated %Control: production of eprint (0) enabled \begin{thebibliography}{79}% \makeatletter \providecommand \@ifxundefined [1]{% \@ifx{#1\undefined} }% \providecommand \@ifnum [1]{% \ifnum #1\expandafter \@firstoftwo \else \expandafter \@secondoftwo \fi }% \providecommand \@ifx [1]{% \ifx #1\expandafter \@firstoftwo \else \expandafter \@secondoftwo \fi }% \providecommand \natexlab [1]{#1}% \providecommand \enquote [1]{``#1''}% \providecommand \bibnamefont [1]{#1}% \providecommand \bibfnamefont [1]{#1}% \providecommand \citenamefont [1]{#1}% \providecommand \href@noop [0]{\@secondoftwo}% \providecommand \href [0]{\begingroup \@sanitize@url \@href}% \providecommand \@href[1]{\@@startlink{#1}\@@href}% \providecommand \@@href[1]{\endgroup#1\@@endlink}% \providecommand \@sanitize@url [0]{\catcode `\\12\catcode `\$12\catcode `\&12\catcode `\#12\catcode `\^12\catcode `\_12\catcode `\%12\relax}% \providecommand \@@startlink[1]{}% \providecommand \@@endlink[0]{}% \providecommand \url [0]{\begingroup\@sanitize@url \@url }% \providecommand \@url [1]{\endgroup\@href {#1}{\urlprefix }}% \providecommand \urlprefix [0]{URL }% \providecommand \Eprint [0]{\href }% \providecommand \doibase [0]{https://doi.org/}% \providecommand \selectlanguage [0]{\@gobble}% \providecommand \bibinfo [0]{\@secondoftwo}% \providecommand \bibfield [0]{\@secondoftwo}% \providecommand \translation [1]{[#1]}% \providecommand \BibitemOpen [0]{}% \providecommand \bibitemStop [0]{}% \providecommand \bibitemNoStop [0]{.\EOS\space}% \providecommand \EOS [0]{\spacefactor3000\relax}% \providecommand \BibitemShut [1]{\csname bibitem#1\endcsname}% \let\auto@bib@innerbib\@empty % \bibitem [{\citenamefont {Gando}\ \emph {et~al.}(2013)\citenamefont {Gando} \emph {et~al.}}]{Gando:2013nba}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Gando}} \emph {et~al.} (\bibinfo {collaboration} {KamLAND}),\ }\href {https://doi.org/10.1103/PhysRevD.88.033001} {\bibfield {journal} {\bibinfo {journal} {\prd}\ }\textbf {\bibinfo {volume} {88}},\ \bibinfo {pages} {033001} (\bibinfo {year} {2013})},\ \Eprint {https://arxiv.org/abs/1303.4667} {arXiv:1303.4667} \BibitemShut {NoStop}% %%CITATION = ARXIV:1303.4667;%% \bibitem [{\citenamefont {An}\ \emph {et~al.}(2017)\citenamefont {An} \emph {et~al.}}]{An:2016srz}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {F.~P.}\ \bibnamefont {An}} \emph {et~al.} (\bibinfo {collaboration} {Daya Bay}),\ }\href {https://doi.org/10.1088/1674-1137/41/1/013002} {\bibfield {journal} {\bibinfo {journal} {Chin. 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J.}\ }\textbf {\bibinfo {volume} {496}},\ \bibinfo {pages} {505} (\bibinfo {year} {1998})}\BibitemShut {NoStop}% %%CITATION = ASJOA,496,505;%% \bibitem [{\citenamefont {Kaether}\ \emph {et~al.}(2010)\citenamefont {Kaether}, \citenamefont {Hampel}, \citenamefont {Heusser}, \citenamefont {Kiko},\ and\ \citenamefont {Kirsten}}]{Kaether:2010ag}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {F.}~\bibnamefont {Kaether}}, \bibinfo {author} {\bibfnamefont {W.}~\bibnamefont {Hampel}}, \bibinfo {author} {\bibfnamefont {G.}~\bibnamefont {Heusser}}, \bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Kiko}},\ and\ \bibinfo {author} {\bibfnamefont {T.}~\bibnamefont {Kirsten}},\ }\href {https://doi.org/10.1016/j.physletb.2010.01.030} {\bibfield {journal} {\bibinfo {journal} {\plb}\ }\textbf {\bibinfo {volume} {685}},\ \bibinfo {pages} {47} (\bibinfo {year} {2010})},\ \Eprint {https://arxiv.org/abs/1001.2731} {arXiv:1001.2731} \BibitemShut {NoStop}% %%CITATION = ARXIV:1001.2731;%% \bibitem [{\citenamefont {Abdurashitov}\ \emph {et~al.}(2009)\citenamefont {Abdurashitov} \emph {et~al.}}]{Abdurashitov:2009tn}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~N.}\ \bibnamefont {Abdurashitov}} \emph {et~al.} (\bibinfo {collaboration} {SAGE}),\ }\href {https://doi.org/10.1103/PhysRevC.80.015807} {\bibfield {journal} {\bibinfo {journal} {Phys. 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\BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Ikeda}},\ }\href {https://doi.org/10.5281/zenodo.1286858} {\bibinfo {title} {Solar neutrino measurements with super-kamiokande}} (\bibinfo {year} {2018}),\ \bibinfo {note} {\textit{Neutrino 2018}, Heidelberg, June 5, 2018.}\BibitemShut {Stop}% \bibitem [{\citenamefont {Bellini}\ \emph {et~al.}(2011)\citenamefont {Bellini} \emph {et~al.}}]{Bellini:2011rx}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont {Bellini}} \emph {et~al.},\ }\href {https://doi.org/10.1103/PhysRevLett.107.141302} {\bibfield {journal} {\bibinfo {journal} {\prl}\ }\textbf {\bibinfo {volume} {107}},\ \bibinfo {pages} {141302} (\bibinfo {year} {2011})},\ \Eprint {https://arxiv.org/abs/1104.1816} {arXiv:1104.1816} \BibitemShut {NoStop}% %%CITATION = ARXIV:1104.1816;%% \bibitem [{\citenamefont {Bellini}\ \emph {et~al.}(2010)\citenamefont {Bellini} \emph {et~al.}}]{Bellini:2008mr}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont {Bellini}} \emph {et~al.} (\bibinfo {collaboration} {Borexino}),\ }\href {https://doi.org/10.1103/PhysRevD.82.033006} {\bibfield {journal} {\bibinfo {journal} {\prd}\ }\textbf {\bibinfo {volume} {82}},\ \bibinfo {pages} {033006} (\bibinfo {year} {2010})},\ \Eprint {https://arxiv.org/abs/0808.2868} {arXiv:0808.2868} \BibitemShut {NoStop}% %%CITATION = ARXIV:0808.2868;%% \bibitem [{\citenamefont {Bellini}\ \emph {et~al.}(2014)\citenamefont {Bellini} \emph {et~al.}}]{Bellini:2014uqa}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {G.}~\bibnamefont {Bellini}} \emph {et~al.} (\bibinfo {collaboration} {Borexino}),\ }\href {https://doi.org/10.1038/nature13702} {\bibfield {journal} {\bibinfo {journal} {Nature}\ }\textbf {\bibinfo {volume} {512}},\ \bibinfo {pages} {383} (\bibinfo {year} {2014})}\BibitemShut {NoStop}% %%CITATION = NATUA,512,383;%% \bibitem [{\citenamefont {Aartsen}\ \emph {et~al.}(2015)\citenamefont {Aartsen} \emph {et~al.}}]{Aartsen:2014yll}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {M.~G.}\ \bibnamefont {Aartsen}} \emph {et~al.} (\bibinfo {collaboration} {IceCube}),\ }\href {https://doi.org/10.1103/PhysRevD.91.072004} {\bibfield {journal} {\bibinfo {journal} {\prd}\ }\textbf {\bibinfo {volume} {91}},\ \bibinfo {pages} {072004} (\bibinfo {year} {2015})},\ \Eprint {https://arxiv.org/abs/1410.7227} {arXiv:1410.7227} \BibitemShut {NoStop}% %%CITATION = ARXIV:1410.7227;%% \bibitem [{\citenamefont {Abe}\ \emph {et~al.}(2018)\citenamefont {Abe} \emph {et~al.}}]{Abe:2017aap}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {K.}~\bibnamefont {Abe}} \emph {et~al.} (\bibinfo {collaboration} {Super-Kamiokande}),\ }\href {https://doi.org/10.1103/PhysRevD.97.072001} {\bibfield {journal} {\bibinfo {journal} {\prd}\ }\textbf {\bibinfo {volume} {97}},\ \bibinfo {pages} {072001} (\bibinfo {year} {2018})},\ \Eprint {https://arxiv.org/abs/1710.09126} {arXiv:1710.09126} \BibitemShut {NoStop}% \bibitem [{\citenamefont {Wong}(2011)}]{Wong:2011ip}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {Y.~Y.}\ \bibnamefont {Wong}},\ }\href {https://doi.org/10.1146/annurev-nucl-102010-130252} {\bibfield {journal} {\bibinfo {journal} {\arnps}\ }\textbf {\bibinfo {volume} {61}},\ \bibinfo {pages} {69} (\bibinfo {year} {2011})},\ \Eprint {https://arxiv.org/abs/1111.1436} {arXiv:1111.1436} \BibitemShut {NoStop}% \bibitem [{\citenamefont {Lesgourgues}\ and\ \citenamefont {Pastor}(2014)}]{Lesgourgues:2014zoa}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Lesgourgues}}\ and\ \bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Pastor}},\ }\href {https://doi.org/10.1088/1367-2630/16/6/065002} {\bibfield {journal} {\bibinfo {journal} {\njp}\ }\textbf {\bibinfo {volume} {16}},\ \bibinfo {pages} {065002} (\bibinfo {year} {2014})},\ \Eprint {https://arxiv.org/abs/1404.1740} {arXiv:1404.1740} \BibitemShut {NoStop}% \bibitem [{\citenamefont {Vagnozzi}\ \emph {et~al.}(2017)\citenamefont {Vagnozzi}, \citenamefont {Giusarma}, \citenamefont {Mena}, \citenamefont {Freese}, \citenamefont {Gerbino}, \citenamefont {Ho},\ and\ \citenamefont {Lattanzi}}]{Vagnozzi:2017ovm}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {S.}~\bibnamefont {Vagnozzi}}, \emph {et~al.},\ }\href {https://doi.org/10.1103/PhysRevD.96.123503} {\bibfield {journal} {\bibinfo {journal} {\prd}\ }\textbf {\bibinfo {volume} {96}},\ \bibinfo {pages} {123503} (\bibinfo {year} {2017})},\ \Eprint {https://arxiv.org/abs/1701.08172} {arXiv:1701.08172} \BibitemShut {NoStop}% \bibitem [{\citenamefont {Aghanim}\ \emph {et~al.}(2020{\natexlab{a}})\citenamefont {Aghanim} \emph {et~al.}}]{Aghanim:2018eyx}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {N.}~\bibnamefont {Aghanim}} \emph {et~al.} (\bibinfo {collaboration} {Planck}),\ }\href 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Not. Roy. Astron. Soc.}\ }\textbf {\bibinfo {volume} {473}},\ \bibinfo {pages} {4773} (\bibinfo {year} {2018})},\ \Eprint {https://arxiv.org/abs/1705.06373} {arXiv:1705.06373} \BibitemShut {NoStop}% \bibitem [{\citenamefont {{Bautista}}\ \emph {et~al.}(2018)\citenamefont {{Bautista}}, \citenamefont {{Vargas-Maga{\~n}a}}, \citenamefont {{Dawson}}, \citenamefont {{Percival}}, \citenamefont {{Brinkmann}}, \citenamefont {{Brownstein}}, \citenamefont {{Camacho}}, \citenamefont {{Comparat}}, \citenamefont {{Gil-Mar{\'\i}n}}, \citenamefont {{Mueller}}, \citenamefont {{Newman}}, \citenamefont {{Prakash}}, \citenamefont {{Ross}}, \citenamefont {{Schneider}}, \citenamefont {{Seo}}, \citenamefont {{Tinker}}, \citenamefont {{Tojeiro}}, \citenamefont {{Zhai}},\ and\ \citenamefont {{Zhao}}}]{Bautista_2018}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~E.}\ \bibnamefont {{Bautista}}}, \emph {et~al.},\ }\href {https://doi.org/10.3847/1538-4357/aacea5} {\bibfield {journal} {\bibinfo {journal} 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{journal} {\aap}\ }\textbf {\bibinfo {volume} {629}},\ \bibinfo {eid} {A86} (\bibinfo {year} {2019})},\ \Eprint {https://arxiv.org/abs/1904.03430} {arXiv:1904.03430} \BibitemShut {NoStop}% \bibitem [{\citenamefont {{Abbott}}\ \emph {et~al.}(2019)\citenamefont {{Abbott}}, \citenamefont {{Abdalla}}, \citenamefont {{Alarcon}}, \citenamefont {{Allam}}, \citenamefont {{Andrade-Oliveira}}, \citenamefont {{Annis}}, \citenamefont {{Avila}}, \citenamefont {{Banerji}}, \citenamefont {{Banik}}, \citenamefont {{Bechtol}}, \citenamefont {{Bernstein}}, \citenamefont {{Bernstein}}, \citenamefont {{Bertin}}, \citenamefont {{Brooks}}, \citenamefont {{Buckley-Geer}}, \citenamefont {{Burke}}, \citenamefont {{Camacho}}, \citenamefont {{Carnero Rosell}}, \citenamefont {{Carrasco Kind}}, \citenamefont {{Carretero}}, \citenamefont {{Castander}}, \citenamefont {{Cawthon}}, \citenamefont {{Chan}}, \citenamefont {{Crocce}}, \citenamefont {{Cunha}}, \citenamefont {{D'Andrea}}, \citenamefont {{da Costa}}, \citenamefont {{Davis}}, \citenamefont {{De Vicente}}, \citenamefont {{DePoy}}, \citenamefont {{Desai}}, \citenamefont {{Diehl}}, \citenamefont {{Doel}}, \citenamefont {{Drlica-Wagner}}, \citenamefont {{Eifler}}, \citenamefont {{Elvin-Poole}}, \citenamefont {{Estrada}}, \citenamefont {{Evrard}}, \citenamefont {{Flaugher}}, \citenamefont {{Fosalba}}, \citenamefont {{Frieman}}, \citenamefont {{Garc{\'\i}a-Bellido}}, \citenamefont {{Gaztanaga}}, \citenamefont {{Gerdes}}, \citenamefont {{Giannantonio}}, \citenamefont {{Gruen}}, \citenamefont {{Gruendl}}, \citenamefont {{Gschwend}}, \citenamefont {{Gutierrez}}, \citenamefont {{Hartley}}, \citenamefont {{Hollowood}}, \citenamefont {{Honscheid}}, \citenamefont {{Hoyle}}, \citenamefont {{Jain}}, \citenamefont {{James}}, \citenamefont {{Jeltema}}, \citenamefont {{Johnson}}, \citenamefont {{Kent}}, \citenamefont {{Kokron}}, \citenamefont {{Krause}}, \citenamefont {{Kuehn}}, \citenamefont {{Kuhlmann}}, \citenamefont {{Kuropatkin}}, \citenamefont 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\citenamefont {{Tarle}}, \citenamefont {{Thomas}}, \citenamefont {{Troxel}}, \citenamefont {{Tucker}}, \citenamefont {{Vikram}}, \citenamefont {{Walker}}, \citenamefont {{Wechsler}}, \citenamefont {{Weller}}, \citenamefont {{Yanny}},\ and\ \citenamefont {{Zhang}}}]{Abbott_2018}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {T.~M.~C.}\ \bibnamefont {{Abbott}}}, \emph {et~al.},\ }\href {https://doi.org/10.1093/mnras/sty3351} {\bibfield {journal} {\bibinfo {journal} {\mnras}\ }\textbf {\bibinfo {volume} {483}},\ \bibinfo {pages} {4866} (\bibinfo {year} {2019})},\ \Eprint {https://arxiv.org/abs/1712.06209} {arXiv:1712.06209} \BibitemShut {NoStop}% \bibitem [{\citenamefont {Riess}\ \emph {et~al.}(2019)\citenamefont {Riess}, \citenamefont {Casertano}, \citenamefont {Yuan}, \citenamefont {Macri},\ and\ \citenamefont {Scolnic}}]{Riess:2019cxk}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {A.~G.}\ \bibnamefont {Riess}}, \bibinfo {author} {\bibfnamefont 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{\bibfnamefont {K.~C.}\ \bibnamefont {{Wong}}}, \emph {et~al.},\ }\href {https://doi.org/10.1093/mnras/stz3094} {\bibfield {journal} {\bibinfo {journal} {\mnras}\ }\textbf {\bibinfo {volume} {498}},\ \bibinfo {pages} {1420} (\bibinfo {year} {2020})},\ \Eprint {https://arxiv.org/abs/1907.04869} {arXiv:1907.04869} \BibitemShut {NoStop}% \bibitem [{\citenamefont {{Freedman}}\ \emph {et~al.}(2019)\citenamefont {{Freedman}}, \citenamefont {{Madore}}, \citenamefont {{Hatt}}, \citenamefont {{Hoyt}}, \citenamefont {{Jang}}, \citenamefont {{Beaton}}, \citenamefont {{Burns}}, \citenamefont {{Lee}}, \citenamefont {{Monson}}, \citenamefont {{Neeley}}, \citenamefont {{Phillips}}, \citenamefont {{Rich}},\ and\ \citenamefont {{Seibert}}}]{2019ApJ...882...34F}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {W.~L.}\ \bibnamefont {{Freedman}}}, \emph {et~al.},\ }\href {https://doi.org/10.3847/1538-4357/ab2f73} {\bibfield {journal} {\bibinfo {journal} {\apj}\ }\textbf {\bibinfo 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{arXiv:2007.08991} \BibitemShut {NoStop}% \bibitem [{\citenamefont {de~Salas}\ \emph {et~al.}(2021)\citenamefont {de~Salas}, \citenamefont {Forero}, \citenamefont {Gariazzo}, \citenamefont {Mart\'\i{}nez-Mirav\'e}, \citenamefont {Mena}, \citenamefont {Ternes}, \citenamefont {T\'ortola},\ and\ \citenamefont {Valle}}]{deSalas:2020pgw}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {de~Salas}}, \emph {et~al.},\ }\href {https://doi.org/10.1007/JHEP02(2021)071} {\bibfield {journal} {\bibinfo {journal} {\jhep}\ }\textbf {\bibinfo {volume} {02}},\ \bibinfo {pages} {071} (\bibinfo {year} {2021})},\ \Eprint {https://arxiv.org/abs/2006.11237} {arXiv:2006.11237} \BibitemShut {NoStop}% \bibitem [{\citenamefont {Aker}\ \emph {et~al.}(2019)\citenamefont {Aker} \emph {et~al.}}]{Aker:2019uuj}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Aker}} \emph {et~al.} (\bibinfo {collaboration} {KATRIN}),\ }\href 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Workgroup, \textit{Supplementary Data: Strengthening the bound on the mass of the lightest neutrino with terrestrial and cosmological experiments}, (2020), \href{https://doi.org/10.5281/zenodo.4005381}{\nolinkurl{https://doi.org/10.5281/zenodo.4005381}}}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Hunter}(2007)}]{Hunter:2007}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {J.~D.}\ \bibnamefont {Hunter}},\ }\href {https://doi.org/10.1109/MCSE.2007.55} {\bibfield {journal} {\bibinfo {journal} {Computing in Science \& Engineering}\ }\textbf {\bibinfo {volume} {9}},\ \bibinfo {pages} {90} (\bibinfo {year} {2007})}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Lewis}(2019)}]{Lewis:2019xzd}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {A.}~\bibnamefont {Lewis}},\ }\href@noop {} {\ (\bibinfo {year} {2019})},\ \Eprint {https://arxiv.org/abs/1910.13970} {arXiv:1910.13970} \BibitemShut {NoStop}% \bibitem [{\citenamefont {{Scott}}(2012)}]{pippi}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {{Scott}}},\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {\epjp}\ }\textbf {\bibinfo {volume} {127}},\ \bibinfo {pages} {138} (\bibinfo {year} {2012})},\ \Eprint {https://arxiv.org/abs/1206.2245} {arXiv:1206.2245} \BibitemShut {NoStop}% \bibitem [{\citenamefont {Carron}(2013)}]{Carron_2013}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {J.}~\bibnamefont {Carron}},\ }\href {https://doi.org/10.1051/0004-6361/201220538} {\bibfield {journal} {\bibinfo {journal} {Astronomy \& Astrophysics}\ }\textbf {\bibinfo {volume} {551}},\ \bibinfo {pages} {A88} (\bibinfo {year} {2013})}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Howlett}\ \emph {et~al.}(2017)\citenamefont {Howlett}, \citenamefont {Staveley-Smith},\ and\ \citenamefont {Blake}}]{Howlett_2016}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {C.}~\bibnamefont {Howlett}}, \bibinfo {author} {\bibfnamefont {L.}~\bibnamefont {Staveley-Smith}},\ and\ \bibinfo {author} {\bibfnamefont {C.}~\bibnamefont {Blake}},\ }\href {https://doi.org/10.1093/mnras/stw2466} {\bibfield {journal} {\bibinfo {journal} {Monthly Notices of the Royal Astronomical Society}\ }\textbf {\bibinfo {volume} {464}},\ \bibinfo {pages} {2517–2544} (\bibinfo {year} {2017})}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Tegmark}(1997)}]{Tegmark_1997}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {M.}~\bibnamefont {Tegmark}},\ }\href {https://doi.org/10.1103/physrevlett.79.3806} {\bibfield {journal} {\bibinfo {journal} {Physical Review Letters}\ }\textbf {\bibinfo {volume} {79}},\ \bibinfo {pages} {3806–3809} (\bibinfo {year} {1997})}\BibitemShut {NoStop}% \bibitem [{\citenamefont {Hinton}\ \emph {et~al.}(2017)\citenamefont {Hinton}, \citenamefont {Kazin}, \citenamefont {Davis}, \citenamefont {Blake}, \citenamefont {Brough}, \citenamefont {Colless}, \citenamefont {Couch}, \citenamefont 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\bibitem [{\citenamefont {{Athron}}\ \emph {et~al.}(2018{\natexlab{b}})\citenamefont {{Athron}}, \citenamefont {{Bal{\'a}zs}}, \citenamefont {{Bringmann}}, \citenamefont {{Buckley}}, \citenamefont {{Chrz{\c a}szcz}}, \citenamefont {{Conrad}}, \citenamefont {{Cornell}}, \citenamefont {{Dal}}, \citenamefont {{Dickinson}}, \citenamefont {{Edsj{\"o}}}, \citenamefont {{Farmer}}, \citenamefont {{Gonzalo}}, \citenamefont {{Jackson}}, \citenamefont {{Krislock}}, \citenamefont {{Kvellestad}}, \citenamefont {{Lundberg}}, \citenamefont {{McKay}}, \citenamefont {{Mahmoudi}}, \citenamefont {{Martinez}}, \citenamefont {{Putze}}, \citenamefont {{Raklev}}, \citenamefont {{Ripken}}, \citenamefont {{Rogan}}, \citenamefont {{Saavedra}}, \citenamefont {{Savage}}, \citenamefont {{Scott}}, \citenamefont {{Seo}}, \citenamefont {{Serra}}, \citenamefont {{Weniger}}, \citenamefont {{White}},\ and\ \citenamefont {{Wild}}}]{gambit_addendum}% \BibitemOpen \bibfield {author} {\bibinfo {author} {\bibfnamefont {P.}~\bibnamefont {{Athron}}}, \emph {et~al.} (\bibinfo {collaboration} {\GB Collaboration}),\ }\href@noop {} {\bibfield {journal} {\bibinfo {journal} {\epjc}\ }\textbf {\bibinfo {volume} {78}},\ \bibinfo {pages} {98} (\bibinfo {year} {2018}{\natexlab{b}})},\ \bibinfo {note} {addendum to \cite{gambit}},\ \Eprint {https://arxiv.org/abs/1705.07908} {arXiv:1705.07908} \BibitemShut {NoStop}% \end{thebibliography}% ``` 5. **Author Information:** - Lead Author: {'name': 'The GAMBIT Cosmology Workgroup'} - Full Authors List: ```yaml The GAMBIT Cosmology Workgroup: {} ':': {} "Patrick St\xF6cker": {} "Csaba Bal\xE1zs": {} Sanjay Bloor: {} Torsten Bringmann: {} "Tom\xE1s E. Gonzalo": {} Will Handley: pi: start: 2020-10-01 thesis: null postdoc: start: 2016-10-01 end: 2020-10-01 thesis: null phd: start: 2012-10-01 end: 2016-09-30 supervisors: - Anthony Lasenby - Mike Hobson thesis: 'Kinetic initial conditions for inflation: theory, observation and methods' original_image: images/originals/will_handley.jpeg image: /assets/group/images/will_handley.jpg links: Webpage: https://willhandley.co.uk Selim Hotinli: {} Cullan Howlett: {} Felix Kahlhoefer: {} Janina J. Renk: {} Pat Scott: {} Aaron C. Vincent: {} Martin White: {} ``` This YAML file provides a concise snapshot of an academic research group. It lists members by name along with their academic roles—ranging from Part III and summer projects to MPhil, PhD, and postdoctoral positions—with corresponding dates, thesis topics, and supervisor details. Supplementary metadata includes image paths and links to personal or departmental webpages. A dedicated "coi" section profiles senior researchers, highlighting the group’s collaborative mentoring network and career trajectories in cosmology, astrophysics, and Bayesian data analysis. ==================================================================================== Final Output Instructions ==================================================================================== - 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. - Validate that every bibliographic reference with a DOI or arXiv identifier is converted into a Markdown link as per the examples. - Validate that every Markdown author link corresponds to a link in the author information block. - Before finalizing, confirm that no LaTeX citation commands or other undesired formatting remain. - Before finalizing, confirm that the link to the paper itself [2009.03287](https://arxiv.org/abs/2009.03287) is featured in the first sentence. Generate only the final Markdown output that meets all these requirements. {% endraw %}