{% 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: "Comparison of dynamical dark energy with ΛCDM in light of DESI
DR2"
date: 2025-03-21
categories: papers
---
Content generated by [gemini-1.5-pro](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/content/2025-03-21-2503.17342.txt).
Image generated by [imagen-3.0-generate-002](https://deepmind.google/technologies/gemini/) using [this prompt](/prompts/images/2025-03-21-2503.17342.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': 'A. N. Ormondroyd'}). 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 [2503.17342](https://arxiv.org/abs/2503.17342) 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
---
The Handley Research Group is dedicated to advancing our understanding of the Universe through the development and application of cutting-edge artificial intelligence and Bayesian statistical inference methods. Our research spans a wide range of cosmological topics, from the very first moments of the Universe to the nature of dark matter and dark energy, with a particular focus on analyzing complex datasets from next-generation surveys.
## Research Focus
Our core research revolves around developing innovative methodologies for analyzing large-scale cosmological datasets. We specialize in Simulation-Based Inference (SBI), a powerful technique that leverages our ability to simulate realistic universes to perform robust parameter inference and model comparison, even when likelihood functions are intractable ([LSBI framework](https://arxiv.org/abs/2501.03921)). This focus allows us to tackle complex astrophysical and instrumental systematics that are challenging to model analytically ([Foreground map errors](https://arxiv.org/abs/2211.10448)).
A key aspect of our work is the development of next-generation SBI tools ([Gradient-guided Nested Sampling](https://arxiv.org/abs/2312.03911)), particularly those based on neural ratio estimation. These methods offer significant advantages in efficiency and scalability for high-dimensional inference problems ([NRE-based SBI](https://arxiv.org/abs/2207.11457)). We are also pioneering the application of these methods to the analysis of Cosmic Microwave Background ([CMB](https://arxiv.org/abs/1908.00906)) data, Baryon Acoustic Oscillations ([BAO](https://arxiv.org/abs/1701.08165)) from surveys like DESI and 4MOST, and gravitational wave observations.
Our AI initiatives extend beyond standard density estimation to encompass a broader range of machine learning techniques, such as:
* **Emulator Development:** We develop fast and accurate emulators of complex astrophysical signals ([globalemu](https://arxiv.org/abs/2104.04336)) for efficient parameter exploration and model comparison ([Neural network emulators](https://arxiv.org/abs/2503.13263)).
* **Bayesian Neural Networks:** We explore the full posterior distribution of Bayesian neural networks for improved generalization and interpretability ([BNN marginalisation](https://arxiv.org/abs/2205.11151)).
* **Automated Model Building:** We are developing novel techniques to automate the process of building and testing theoretical cosmological models using a combination of symbolic computation and machine learning ([Automated model building](https://arxiv.org/abs/2006.03581)).
Additionally, we are active in the development and application of advanced sampling methods like nested sampling ([Nested sampling review](https://arxiv.org/abs/2205.15570)), including dynamic nested sampling ([Dynamic nested sampling](https://arxiv.org/abs/1704.03459)) and its acceleration through techniques like posterior repartitioning ([Accelerated nested sampling](https://arxiv.org/abs/2411.17663)).
## Highlight Achievements
Our group has a strong publication record in high-impact journals and on the arXiv preprint server. Some key highlights include:
* Development of novel AI-driven methods for analyzing the 21-cm signal from the Cosmic Dawn ([21-cm analysis](https://arxiv.org/abs/2201.11531)).
* Contributing to the Planck Collaboration's analysis of CMB data ([Planck 2018](https://arxiv.org/abs/1807.06205)).
* Development of the PolyChord nested sampling software ([PolyChord](https://arxiv.org/abs/1506.00171)), which is now widely used in cosmological analyses.
* Contributions to the GAMBIT global fitting framework ([GAMBIT CosmoBit](https://arxiv.org/abs/2009.03286)).
* Applying SBI to constrain dark matter models ([Dirac Dark Matter EFTs](https://arxiv.org/abs/2106.02056)).
## Future Directions
We are committed to pushing the boundaries of cosmological analysis through our ongoing and future projects, including:
* Applying SBI to test extensions of General Relativity ([Modified Gravity](https://arxiv.org/abs/2006.03581)).
* Developing AI-driven tools for efficient and robust calibration of cosmological experiments ([Calibration for astrophysical experimentation](https://arxiv.org/abs/2307.00099)).
* Exploring the use of transformers and large language models for automating the process of cosmological model building.
* Applying our expertise to the analysis of data from next-generation surveys like Euclid, the Vera Rubin Observatory, and the Square Kilometre Array. This will allow us to probe the nature of dark energy with increased precision ([Dynamical Dark Energy](https://arxiv.org/abs/2503.08658)), search for parity violation in the large-scale structure ([Parity Violation](https://arxiv.org/abs/2410.16030)), and explore a variety of other fundamental questions.
Content generated by [gemini-1.5-pro](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/2503.17342v1
guidislink: true
link: http://arxiv.org/abs/2503.17342v1
updated: '2025-03-21T17:45:04Z'
updated_parsed: !!python/object/apply:time.struct_time
- !!python/tuple
- 2025
- 3
- 21
- 17
- 45
- 4
- 4
- 80
- 0
- tm_zone: null
tm_gmtoff: null
published: '2025-03-21T17:45:04Z'
published_parsed: !!python/object/apply:time.struct_time
- !!python/tuple
- 2025
- 3
- 21
- 17
- 45
- 4
- 4
- 80
- 0
- tm_zone: null
tm_gmtoff: null
title: "Comparison of dynamical dark energy with \u039BCDM in light of DESI\n DR2"
title_detail: !!python/object/new:feedparser.util.FeedParserDict
dictitems:
type: text/plain
language: null
base: ''
value: "Comparison of dynamical dark energy with \u039BCDM in light of DESI\n\
\ DR2"
summary: 'We present an updated reconstruction of the dark energy equation of state,
$w(a)$, using the newly released DESI DR2 Baryon Acoustic Oscillation (BAO)
data in combination with Pantheon+ and DES5Y Type Ia supernovae measurements,
respectively. Building on our previous analysis in arXiv:2503.08658, which
employed a nonparametric flexknot reconstruction approach, we examine whether
the evidence for dynamical dark energy persists with the improved precision of
the DESI DR2 dataset. We find that while the overall qualitative structure of
$w(a)$ remains consistent with our earlier findings, the statistical support
for dynamical dark energy is reduced when considering DESI DR2 data alone,
particularly for more complex flexknot models with higher numbers of knots.
However, the evidence for simpler dynamical models, such as $w$CDM and CPL
(which correspond to $n=1$ and $n=2$ knots respectively), increases relative to
$\Lambda$CDM with DESI DR2 alone, consistent with previous DESI analyses. When
combined with Pantheon+ data, the conclusions remain broadly consistent with
our earlier work, but the inclusion of DES5Y supernovae data leads to an
increase of preference for flexknot models with more than two knots, placing
$w$CDM and CPL on par with $\Lambda$CDM.'
summary_detail: !!python/object/new:feedparser.util.FeedParserDict
dictitems:
type: text/plain
language: null
base: ''
value: 'We present an updated reconstruction of the dark energy equation of
state,
$w(a)$, using the newly released DESI DR2 Baryon Acoustic Oscillation (BAO)
data in combination with Pantheon+ and DES5Y Type Ia supernovae measurements,
respectively. Building on our previous analysis in arXiv:2503.08658, which
employed a nonparametric flexknot reconstruction approach, we examine whether
the evidence for dynamical dark energy persists with the improved precision
of
the DESI DR2 dataset. We find that while the overall qualitative structure
of
$w(a)$ remains consistent with our earlier findings, the statistical support
for dynamical dark energy is reduced when considering DESI DR2 data alone,
particularly for more complex flexknot models with higher numbers of knots.
However, the evidence for simpler dynamical models, such as $w$CDM and CPL
(which correspond to $n=1$ and $n=2$ knots respectively), increases relative
to
$\Lambda$CDM with DESI DR2 alone, consistent with previous DESI analyses.
When
combined with Pantheon+ data, the conclusions remain broadly consistent with
our earlier work, but the inclusion of DES5Y supernovae data leads to an
increase of preference for flexknot models with more than two knots, placing
$w$CDM and CPL on par with $\Lambda$CDM.'
authors:
- !!python/object/new:feedparser.util.FeedParserDict
dictitems:
name: A. N. Ormondroyd
- !!python/object/new:feedparser.util.FeedParserDict
dictitems:
name: W. J. Handley
- !!python/object/new:feedparser.util.FeedParserDict
dictitems:
name: M. P. Hobson
- !!python/object/new:feedparser.util.FeedParserDict
dictitems:
name: A. N. Lasenby
author_detail: !!python/object/new:feedparser.util.FeedParserDict
dictitems:
name: A. N. Lasenby
author: A. N. Lasenby
arxiv_comment: 5 pages, 5 figures, 1 table
links:
- !!python/object/new:feedparser.util.FeedParserDict
dictitems:
href: http://arxiv.org/abs/2503.17342v1
rel: alternate
type: text/html
- !!python/object/new:feedparser.util.FeedParserDict
dictitems:
title: pdf
href: http://arxiv.org/pdf/2503.17342v1
rel: related
type: application/pdf
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
```
3. **Paper Source (TeX):**
```tex
% mnras_template.tex
%
% LaTeX template for creating an MNRAS paper
%
% v3.0 released 14 May 2015
% (version numbers match those of mnras.cls)
%
% Copyright (C) Royal Astronomical Society 2015
% Authors:
% Keith T. Smith (Royal Astronomical Society)
% Change log
%
% v3.0 May 2015
% Renamed to match the new package name
% Version number matches mnras.cls
% A few minor tweaks to wording
% v1.0 September 2013
% Beta testing only - never publicly released
% First version: a simple (ish) template for creating an MNRAS paper
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Basic setup. Most papers should leave these options alone.
\documentclass[fleqn,usenatbib]{mnras}
% MNRAS is set in Times font. If you don't have this installed (most LaTeX
% installations will be fine) or prefer the old Computer Modern fonts, comment
% out the following line
\usepackage{newtxtext,newtxmath}
% Depending on your LaTeX fonts installation, you might get better results with one of these:
%\usepackage{mathptmx}
%\usepackage{txfonts}
% Use vector fonts, so it zooms properly in on-screen viewing software
% Don't change these lines unless you know what you are doing
\usepackage[T1]{fontenc}
% Allow "Thomas van Noord" and "Simon de Laguarde" and alike to be sorted by "N" and "L" etc. in the bibliography.
% Write the name in the bibliography as "\VAN{Noord}{Van}{van} Noord, Thomas"
\DeclareRobustCommand{\VAN}[3]{#2}
\let\VANthebibliography\thebibliography
\def\thebibliography{\DeclareRobustCommand{\VAN}[3]{##3}\VANthebibliography}
%%%%% AUTHORS - PLACE YOUR OWN PACKAGES HERE %%%%%
% Only include extra packages if you really need them. Common packages are:
\usepackage{graphicx} % Including figure files
\usepackage{amsmath} % Advanced maths commands
\usepackage{siunitx} % units for physical quantities
\usepackage{hyperref} % links to github
% \usepackage[frozencache,cachedir=.]{minted} % code block in appendix
% \usepackage{minted}
\usepackage{multirow, makecell} % used to place images in tensions table
\usepackage[table]{xcolor} % coloured rows in table
\usepackage{color, soul}% Highlighting todo
% \usepackage{amssymb} % Extra maths symbols
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% AUTHORS - PLACE YOUR OWN COMMANDS HERE %%%%%
\newcommand{\ncr}[2]{{}^{#1}C_{#2}}
% Please keep new commands to a minimum, and use \newcommand not \def to avoid
% overwriting existing commands. Example:
%\newcommand{\pcm}{\,cm$^{-2}$} % per cm-squared
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%% TITLE PAGE %%%%%%%%%%%%%%%%%%%
% Title of the paper, and the short title which is used in the headers.
% Keep the title short and informative.
\title[Dynamical Dark Energy in DESI DR2]{Comparison of dynamical dark energy with $\Lambda$CDM in light of DESI DR2}
% The list of authors, and the short list which is used in the headers.
% If you need two or more lines of authors, add an extra line using \newauthor
\author[A.N.~Ormondroyd et al.]{
A.N.~Ormondroyd,$^{1,2}$\thanks{E-mail: ano23@cam.ac.uk}
W.J.~Handley,$^{1,2}$
M.P.~Hobson$^{1}$
and A.N.~Lasenby$^{1,2}$
\\
% List of institutions
$^{1}$Astrophysics Group, Cavendish Laboratory, J.J.~Thomson Avenue, Cambridge, CB3 0HE, UK\\
$^{2}$Kavli Institute for Cosmology, Madingley Road, Cambridge, CB3 0HA, UK\\
}
% These dates will be filled out by the publisher
\date{Accepted XXX. Received YYY; in original form ZZZ}
% Enter the current year, for the copyright statements etc.
\pubyear{2025}
% Don't change these lines
\begin{document}
\label{firstpage}
\pagerange{\pageref{firstpage}--\pageref{lastpage}}
\maketitle
% Abstract of the paper
\begin{abstract}
We present an updated reconstruction of the dark energy equation of state, $w(a)$, using the newly released DESI DR2 Baryon Acoustic Oscillation (BAO) data in combination with Pantheon+ and DES5Y Type Ia supernovae measurements, respectively.
Building on our previous analysis in \cite{2025arXiv250308658O}, which employed a nonparametric flexknot reconstruction approach, we examine whether the evidence for dynamical dark energy persists with the improved precision of the DESI DR2 dataset. We find that while the overall qualitative structure of $w(a)$ remains consistent with our earlier findings, the statistical support for dynamical dark energy is reduced when considering DESI DR2 data alone, particularly for more complex flexknot models with higher numbers of knots.
However, the evidence for simpler dynamical models, such as $w$CDM and CPL (which correspond to $n=1$ and $n=2$ knots respectively), increases relative to $\Lambda$CDM with DESI DR2 alone, consistent with previous DESI analyses.
When combined with Pantheon+ data, the conclusions remain broadly consistent with our earlier work, but the inclusion of DES5Y supernovae data leads to an increase of preference for flexknot models with more than two knots, placing $w$CDM and CPL on par with $\Lambda$CDM.
\end{abstract}
% Select between one and six entries from the list of approved keywords.
% Don't make up new ones.
\begin{keywords}
methods: statistical -- cosmology: dark energy, cosmological parameters
\end{keywords}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%% BODY OF PAPER %%%%%%%%%%%%%%%%%%
\section{Introduction}
The standard model of cosmology, $\Lambda$CDM, has been remarkably successful in explaining a wide range of cosmological observations.
Recent work has reinforced the importance of understanding the nature of dark energy through increasingly precise cosmological measurements.
In our previous study \citep{2025arXiv250308658O}, we employed a nonparametric flexknot reconstruction \cite[originally termed `nodal reconstruction'][]{pkvazquez,devazquez} of the dark energy equation-of-state parameter, $w(a)$, to explore the possibility of dynamical dark energy.
Using a flexible linear-spline approach with free-moving nodes, our analysis of DESI Baryon Acoustic Oscillation (BAO) combined with either Pantheon+ or DES5Y Type Ia supernovae data unexpectedly revealed a W-shaped structure in $w(a)$.
This structure, which deviates from the conventional constant-$w$ ($\Lambda$CDM) picture, raised questions about whether standard parameterisations such as $w$CDM or CPL might be too restrictive to capture the true dynamical behavior of dark energy.
This is acknowledged in the DESI DR2 release \citep{desi2025, desi2i, desi2ii}, which includes an entire paper dedicated to an extended dark energy analysis \citep{desi2de}.
In this update, we investigate how the conclusions of \cite{2025arXiv250308658O} change in light of DESI DR2.
\vfill
\section{Data}\label{sec:data}
\begin{figure}
\centering
\includegraphics[width=0.48\textwidth]{plots/desi3_DR1_comparison_20_wa.pdf}
\caption{
Flexknot reconstruction of $w(a)$ using DESI DR2 BAO data using flexknots, compared to DR1.
Upper left panel: the reconstructed $w(a)$.
The dashed line is the mean of the posterior, and the shaded region is the $1\sigma$ contour.
The overall shape is similar to DR1, but the transition around $a=0.6-0.7$ is less pronounced.
Upper right panel: the evidence for each number of knots $n$, relative to $\Lambda$CDM.
The biggest change is the new data admits a constant $w$ model ($n=1$) as a viable model.
Evidence for models with more than four knots is reduced compared to DR1.
Lower left panel: posterior distributions of $\Omega_\mathrm m$ and $H_0r_\mathrm d$.
Lower right panel: the same reconstruction as the upper left panel, but transformed to $w(z)$.
}\label{fig:desidr12}
\end{figure}
\begin{figure}
\begin{center}
\includegraphics[width=0.48\textwidth]{plots/desi3_20_distances.pdf}
\end{center}
\caption{
BAO distances reconstructed from DESI BAO data.
The left column is DESI DR1, the right column is DESI DR2.
The best-fit $\Lambda$CDM has been subtracted from each set of distances, and the $w(a)$ posteriors are repeated in the bottom two panels.
$1\sigma$ contours are also shown.
It can been seen how the smaller error bars in DR2 have produced a narrower $1\sigma$ contour for the reconstructions.
}\label{fig:distances}
\end{figure}
We combine DESI DR2 BAO data with Pantheon+ \citep{pantheonplus} and DES5Y supernovae \citep{des5y}, respectively.
DESI DR2 cosmological distances are used as they appear in Table~IV of \cite{desi2ii}.
DESI DR1, Pantheon+, and DES5Y data
are used in precisely the same manner as in \cite{2025arXiv250308658O}.
The DESI DR2 BAO improves constraints on cosmic expansion with a larger dataset of galaxies and quasars than DR1.
In addition to the tightening of the error bars compared to the previous release, the Quasar Sample (QSO) now has sufficient signal-to-noise ratio that separate measurements of $D_\mathrm M(z)$ and $D_\mathrm H(z)$ are reported in DR2, whereas in DR1 only a volume-averaged $D_\mathrm V(z)$ value was reported \cite{desi2ii, desiiii}.
\section{Methods}
With these improved DESI DR2 measurements now available, we recap the flexknot-based methodology that enables us to explore dynamical dark energy in a nonparametric way.
In this approach, $w(a)$ is modelled using a flexible linear spline between free-moving nodes.
This technique is well-established in multiple fields within cosmology: it has been used to reconstruct history of the dark energy equation of state from CMB data \citep{sonke, devazquez}, the primordial power spectrum \citep{pkhandley, pkvazquez, pkknottedsky, pkcore, pkplanck13, pkplanck15}, the cosmic reionisation history \citep{flexknotreionization, heimersheimfrb}, galaxy cluster profiles \citep{flexknotclusters}, and the $\SI{21}{\centi\metre}$ signal \citep{heimersheim21cm, shen}.
Unlike dark energy reconstructions such as Gaussian processes \cite{modelagnosticgp, quintom, 2025arXiv250304273J, 2025arXiv250315943G} or cubic splines \citep{2025arXiv250313198B}, flexknots can reconstruct arbitrarily sharp features, and have extremely weak functional correlation structure. Flexknots also have the advantage that the $w$CDM and CPL models correspond to the special cases of $n=1$ and $n=2$ knots, respectively.
\begin{table}
\centering
\rowcolors{2}{}{gray!25}
\begin{tabular}{|l|c|}
\hline
Parameter & Prior \\
\hline
$n$ & $[1, 20]$ \\
$a_{n-1}$ & $0$ \\
$a_{n-2}, \dots, a_1$ & sorted($[a_{n-1}, a_0])$ \\
$a_0$ & $1$ \\
$w_{n-1}, \dots, w_0$ & $[-3, -0.01]$ \\
$\Omega_\mathrm m$ & $[0.01, 0.99]$ \\
$H_0r_\mathrm d$ (DESI)& $[3650, 18250]$ \\
$H_0$ (Ia) & $[20, 100]$ \\
\hline
\end{tabular}
\caption{
Cosmological priors used in this work.
Fixed values are indicated by a single number, while uniform priors are denoted by brackets.
As BAO only depend on the product $H_0r_\mathrm d$, and supernovae depend on $H_0$, those parameters are only included as necessary. Whilst the dynamical dark energy priors are broadly consistent with those in \protect\cite{desi2ii}, these inevitably differ from CPL priors which instead put a uniform prior on the gradient $w_a$.
}
\label{tab:priors}
\end{table}
\begin{figure*}
\centering
\includegraphics[width=0.48\textwidth]{plots/desi3ia_h0_DR1_comparison_20_wa.pdf}
\includegraphics[width=0.48\textwidth]{plots/desi3des5y_DR1_comparison_20_wa.pdf}
\caption{
Similar to Figure~\ref{fig:desidr12}, but comparing DESI DR2 BAO data with Pantheon+ supernovae (left) and DES5Y supernovae (right).
The most significant difference between the DR1 and DR2 reconstructions is the same region of $a$ as in Figure~\ref{fig:desidr12}.
Left four panels: DESI DR2 + Pantheon+, compared to DR1 + Pantheon+.
The evidence for $w$CDM is very similar between DR1 and DR2, but the remaining flexknots are less favoured in DR2.
Right four panels: DESI DR2 + DES5Y, compared to DR1 + DES5Y.
The change is very much the opposite as it was with Pantheon+, with the evidence for all numbers of knots greater than or equal to two have increased significantly, with CPL remaining the preferred model.
}\label{fig:desidr2ia}
\end{figure*}
\begin{figure}
\begin{center}
\includegraphics[width=0.48\textwidth]{plots/desi3ia_h0des5y_tension_i.pdf}
\end{center}
\caption{
Tension quantifications between combinations of datasets. For each knot reconstruction $N$ we compare the tension between DESI (DR1 or DR2) and supernovae (Pantheon+ [left panel] or DES5Y [right panel]). In light of the update from DR1 to DR2, the tension has increased between DESI and Pantheon+ ($\log R$ lower), but remains consistent ($\log R > 0$). For DESI and DES5Y in light of the update from DR1 to DR2 the tension has decreased ($\log R$ higher) and is now consistent $\log R>0$ for all but the $\Lambda$CDM ($N=0$) and $w$CDM ($N=1$) cases .
}\label{fig:tension}
\end{figure}
Posterior samples and evidences were obtained using the nested sampling algorithm \texttt{PolyChord} \citep{skilling2004, polychord1, polychord2}.
A branch of \texttt{fgivenx} was used to produce the functional posterior plots \citep{fgivenx}, and \texttt{anesthetic} was used to process the nested sampling chains \citep{anesthetic}.
As in \cite{2025arXiv250308658O}, $H_0$ and $M_B$ are marginalised over, and the prior on $M_B$ is taken to be uniform and sufficiently wide to contain the entire posterior.
In the DESI analyses \cite{desi2ii, desivi}, it is enforced that $w_0+w_a<0$ to ensure that there is a period of matter domination at high redshifts.
In this work, we take $w_i < 0$ to achieve the same effect.
Table~\ref{tab:priors} lists the cosmological priors used in this work, the same as \cite{2025arXiv250308658O}, which themselves were chosen to remain consistent with those used in \cite{desicrossingstatistics}.
\pagebreak
\section{Results}\label{sec:results}
Figure~\ref{fig:desidr12} shows reconstructions of $w(a)$ from DESI alone, and compares DR1 and DR2.
Figure~\ref{fig:distances} shows the corresponding BAO distances reconstructed from DESI BAO data, compared to the best-fit $\Lambda$CDM model.
The most significant change is not in the shape of the $w(a)$ posterior, but the evidences for each number of knots $n$ in the reconstruction.
The greatest contrast is in the single knot case ($w$CDM), for which there is now a very slight preference relative to $\Lambda$CDM in DR2, whereas $w$CDM was reasonably disfavoured in DR1.
As the number of knots increases, the evidences tend to a lower value for DR2 than for DR1.
This means that DR2 is less supportive than DR1 of the flexknot model.
The most significant change to the reconstructed $w(a)$ is the transition around $a=0.6-0.7$, which is the region containing the two LRG points whose affect was investigated in detail in \cite{2025arXiv250308658O}.
This has moved to slightly higher redshifts, and is tighter than in DR1.
The DR2 reconstructions have a more pronounced transition at slightly higher redshifts between phantom and quintessence than DR1, which continues to be the case when supernovae are included.
Looking specifically, however, at $n=2$ (i.e. the CPL parameterisation), we note that the evidence slightly increases relative to $\Lambda$CDM with DR2 compared to DR1. This matches the conclusion of \cite{desi2ii} that DR2 more strongly supports CPL dark energy over $\Lambda$CDM than DR1, although the overall evidence for both flexknots, and CPL, is marginal.
Figure~\ref{fig:desidr2ia} shows a comparison of results from the DESI DR1/DR2 BAO data when combined with Pantheon+ and DES5Y supernovae, respectively.
The evidences for $w$CDM in DR2 are very similar to those with DR1 and, as when using DESI alone, the evidences tend to a lower value for DR2 than for DR1 as the number of knots $n$ increases.
Most notably, there is now a preference for models with large numbers of knots with DESI DR2 + DES5Y, which was the only combination in \cite{2025arXiv250308658O} which had any evidence in favour of dynamical dark energy, and the CPL model is still favoured.
When combining data it is prudent to check that the datasets are consistent with each other. Here we follow \cite{2025arXiv250308658O} in using the tension analysis developed and deployed in \cite{lemos, hergt, balancingact} via the $\log R$ statistic.
In Figure~\ref{fig:tension} we show the tension quantifications between DESI and supernovae datasets. For DESI vs Pantheon+, there has been a slight increase in tension between DR1 and DR2, but they remain consistent. For DESI vs DES5Y the tension has decreased between DR1 and DR2, and is now consistent for all but the $\Lambda$CDM and $w$CDM cases. In this sense, dynamical dark energy models can be viewed as resolving a discrepancy between DESI and DES5Y data, in addition to providing a better fit to the data.
For reference, we show the non-overlayed reconstructions of $w(a)$ for the remaining combinations of datasets in Figure~\ref{fig:separated}. DESI alone can be seen in the lower panels of Figure~\ref{fig:distances}.
\section{Conclusions}\label{sec:conclusions}
We revisited the dynamical dark energy reconstructions presented in \cite{2025arXiv250308658O} using the newly-released DESI DR2 BAO data in combination with Pantheon+ and DES5Y supernovae measurements, respectively.
Our analysis employed a flexknot methodology to reconstruct the evolution of the dark energy equation of state $w(a)$.
Overall, we find that while the qualitative shape of the reconstructed $w(a)$ remains consistent with our previous work, there is a marked change in the statistical evidence for dynamical dark energy.
The DESI DR2 data alone lead to a reduction in the evidence as compared with DR1 for flexknot models with larger numbers of knots.
However, the evidence for the $w$CDM and CPL models, which correspond to $n=1$ and $n=2$ knots respectively, have increased compared to $\Lambda$CDM with DESI alone, which aligns with the conclusions of \cite{desi2ii}.
When the DESI DR2 BAO data are combined with Pantheon+ supernovae, the conclusions are similar to those in our original work.
However, with DES5Y supernovae, there is now increased evidence for models with a larger number of knots, with evidence for CPL, which remains the preferred model, also increasing, and with $w$CDM remaining on-par with $\Lambda$CDM. In addition to providing a better fit, dynamical dark energy models serve to resolve a discrepancy between DESI and DES5Y data.
\section*{Acknowledgements}
This work was performed using the Cambridge Service for Data Driven Discovery (CSD3), part of which is operated by the University of Cambridge Research Computing on behalf of the STFC DiRAC HPC Facility (\url{www.dirac.ac.uk}).
The DiRAC component of CSD3 was funded by BEIS capital funding via STFC capital grants ST/P002307/1 and ST/R002452/1 and STFC operations grant ST/R00689X/1.
DiRAC is part of the National e-Infrastructure.
The tension calculations in this work made use of \texttt{NumPy} \citep{numpy}, \texttt{SciPy} \citep{scipy}, and \texttt{pandas} \citep{pandaszenodo, pandaspaper}.
The plots were produced in \texttt{matplotlib} \citep{matplotlib}, using the \texttt{smplotlib} template created by \citet{smplotlib}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Data Availability}
The pared-down Python pipeline and nested sampling chains used in this work can be obtained from Zenodo \citep{ormondroyd_2025_15025604}.
%%%%%%%%%%%%%%%%%%%% REFERENCES %%%%%%%%%%%%%%%%%%
% The best way to enter references is to use BibTeX:
\bibliographystyle{mnras}
\bibliography{desi2} % if your bibtex file is called example.bib
% Alternatively you could enter them by hand, like this:
% This method is tedious and prone to error if you have lots of references
%\begin{thebibliography}{99}
%\bibitem[\protect\citeauthoryear{Author}{2012}]{Author2012}
%Author A.~N., 2013, Journal of Improbable Astronomy, 1, 1
%\bibitem[\protect\citeauthoryear{Others}{2013}]{Others2013}
%Others S., 2012, Journal of Interesting Stuff, 17, 198
%\end{thebibliography}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%% APPENDICES %%%%%%%%%%%%%%%%%%%%%
\begin{figure*}
\begin{center}
\includegraphics[width=0.95\textwidth]{plots/all_together.pdf}
\end{center}
\caption{
For reference, non-overlayed reconstructions of $w(a)$ for the remaining combinations of datasets, as in the lower panels of Figure~\protect{\ref{fig:distances}}.
}\label{fig:separated}
\end{figure*}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Don't change these lines
\bsp % typesetting comment
\label{lastpage}
\end{document}
% End of mnras_template.tex
```
4. **Bibliographic Information:**
```bbl
\begin{thebibliography}{}
\makeatletter
\relax
\def\mn@urlcharsother{\let\do\@makeother \do\$\do\&\do\#\do\^\do\_\do\%\do\~}
\def\mn@doi{\begingroup\mn@urlcharsother \@ifnextchar [ {\mn@doi@}
{\mn@doi@[]}}
\def\mn@doi@[#1]#2{\def\@tempa{#1}\ifx\@tempa\@empty \href
{http://dx.doi.org/#2} {doi:#2}\else \href {http://dx.doi.org/#2} {#1}\fi
\endgroup}
\def\mn@eprint#1#2{\mn@eprint@#1:#2::\@nil}
\def\mn@eprint@arXiv#1{\href {http://arxiv.org/abs/#1} {{\tt arXiv:#1}}}
\def\mn@eprint@dblp#1{\href {http://dblp.uni-trier.de/rec/bibtex/#1.xml}
{dblp:#1}}
\def\mn@eprint@#1:#2:#3:#4\@nil{\def\@tempa {#1}\def\@tempb {#2}\def\@tempc
{#3}\ifx \@tempc \@empty \let \@tempc \@tempb \let \@tempb \@tempa \fi \ifx
\@tempb \@empty \def\@tempb {arXiv}\fi \@ifundefined
{mn@eprint@\@tempb}{\@tempb:\@tempc}{\expandafter \expandafter \csname
mn@eprint@\@tempb\endcsname \expandafter{\@tempc}}}
\bibitem[\protect\citeauthoryear{{Aslanyan}, {Price}, {Abazajian} \&
{Easther}}{{Aslanyan} et~al.}{2014}]{pkknottedsky}
{Aslanyan} G., {Price} L.~C., {Abazajian} K.~N., {Easther} R., 2014,
\mn@doi [\jcap] {10.1088/1475-7516/2014/08/052}, \href
{https://ui.adsabs.harvard.edu/abs/2014JCAP...08..052A} {2014, 052}
\bibitem[\protect\citeauthoryear{{Berti}, {Bellini}, {Bonvin}, {Kunz}, {Viel}
\& {Zumalacarregui}}{{Berti} et~al.}{2025}]{2025arXiv250313198B}
{Berti} M., {Bellini} E., {Bonvin} C., {Kunz} M., {Viel} M.,
{Zumalacarregui} M., 2025, arXiv e-prints, \href
{https://ui.adsabs.harvard.edu/abs/2025arXiv250313198B} {p. arXiv:2503.13198}
\bibitem[\protect\citeauthoryear{{Brout} et~al.,}{{Brout}
et~al.}{2022}]{pantheonplus}
{Brout} D., et~al., 2022, \mn@doi [\apj] {10.3847/1538-4357/ac8e04}, \href
{https://ui.adsabs.harvard.edu/abs/2022ApJ...938..110B} {938, 110}
\bibitem[\protect\citeauthoryear{{Calderon} et~al.,}{{Calderon}
et~al.}{2024}]{desicrossingstatistics}
{Calderon} R., et~al., 2024, \mn@doi [\jcap] {10.1088/1475-7516/2024/10/048},
\href {https://ui.adsabs.harvard.edu/abs/2024JCAP...10..048C} {2024, 048}
\bibitem[\protect\citeauthoryear{{DES Collaboration} et~al.,}{{DES
Collaboration} et~al.}{2024}]{des5y}
{DES Collaboration} et~al., 2024, \mn@doi [\apjl] {10.3847/2041-8213/ad6f9f},
\href {https://ui.adsabs.harvard.edu/abs/2024ApJ...973L..14D} {973, L14}
\bibitem[\protect\citeauthoryear{{DESI Collaboration} et~al.,}{{DESI
Collaboration} et~al.}{2024a}]{desiiii}
{DESI Collaboration} et~al., 2024a, \mn@doi [arXiv e-prints]
{10.48550/arXiv.2404.03000}, \href
{https://ui.adsabs.harvard.edu/abs/2024arXiv240403000D} {p. arXiv:2404.03000}
\bibitem[\protect\citeauthoryear{{DESI Collaboration} et~al.,}{{DESI
Collaboration} et~al.}{2024b}]{desivi}
{DESI Collaboration} et~al., 2024b, \mn@doi [arXiv e-prints]
{10.48550/arXiv.2404.03002}, \href
{https://ui.adsabs.harvard.edu/abs/2024arXiv240403002D} {p. arXiv:2404.03002}
\bibitem[\protect\citeauthoryear{{DESI Collaboration} et~al.,}{{DESI
Collaboration} et~al.}{2025a}]{desi2ii}
{DESI Collaboration} et~al., 2025a, arXiv e-prints, \href
{https://ui.adsabs.harvard.edu/abs/2025arXiv250314738D} {p. arXiv:2503.14738}
\bibitem[\protect\citeauthoryear{{DESI Collaboration} et~al.,}{{DESI
Collaboration} et~al.}{2025b}]{desi2i}
{DESI Collaboration} et~al., 2025b, arXiv e-prints, \href
{https://ui.adsabs.harvard.edu/abs/2025arXiv250314739D} {p. arXiv:2503.14739}
\bibitem[\protect\citeauthoryear{{DESI Collaboration} et~al.,}{{DESI
Collaboration} et~al.}{2025c}]{desi2de}
{DESI Collaboration} et~al., 2025c, arXiv e-prints, \href
{https://ui.adsabs.harvard.edu/abs/2025arXiv250314743D} {p. arXiv:2503.14743}
\bibitem[\protect\citeauthoryear{{DESI Collaboration} et~al.,}{{DESI
Collaboration} et~al.}{2025d}]{desi2025}
{DESI Collaboration} et~al., 2025d, arXiv e-prints, \href
{https://ui.adsabs.harvard.edu/abs/2025arXiv250314745D} {p. arXiv:2503.14745}
\bibitem[\protect\citeauthoryear{{Dinda} \& {Maartens}}{{Dinda} \&
{Maartens}}{2025}]{modelagnosticgp}
{Dinda} B.~R., {Maartens} R., 2025, \mn@doi [\jcap]
{10.1088/1475-7516/2025/01/120}, \href
{https://ui.adsabs.harvard.edu/abs/2025JCAP...01..120D} {2025, 120}
\bibitem[\protect\citeauthoryear{{Finelli} et~al.,}{{Finelli}
et~al.}{2018}]{pkcore}
{Finelli} F., et~al., 2018, \mn@doi [\jcap] {10.1088/1475-7516/2018/04/016},
\href {https://ui.adsabs.harvard.edu/abs/2018JCAP...04..016F} {2018, 016}
\bibitem[\protect\citeauthoryear{{Gao}, {Gao}, {Gong} \& {Lu}}{{Gao}
et~al.}{2025}]{2025arXiv250315943G}
{Gao} S., {Gao} Q., {Gong} Y., {Lu} X., 2025, arXiv e-prints, \href
{https://ui.adsabs.harvard.edu/abs/2025arXiv250315943G} {p. arXiv:2503.15943}
\bibitem[\protect\citeauthoryear{{Handley}}{{Handley}}{2019a}]{fgivenx}
{Handley} W., 2019a, {fgivenx: Functional posterior plotter}, Astrophysics
Source Code Library, record ascl:1909.014
\bibitem[\protect\citeauthoryear{Handley}{Handley}{2019b}]{anesthetic}
Handley W., 2019b, \mn@doi [The Journal of Open Source Software]
{10.21105/joss.01414}, 4, 1414
\bibitem[\protect\citeauthoryear{{Handley} \& {Lemos}}{{Handley} \&
{Lemos}}{2019}]{lemos}
{Handley} W., {Lemos} P., 2019, \mn@doi [\prd] {10.1103/PhysRevD.100.043504},
\href {https://ui.adsabs.harvard.edu/abs/2019PhRvD.100d3504H} {100, 043504}
\bibitem[\protect\citeauthoryear{{Handley}, {Hobson} \& {Lasenby}}{{Handley}
et~al.}{2015a}]{polychord1}
{Handley} W.~J., {Hobson} M.~P., {Lasenby} A.~N., 2015a, \mn@doi [\mnras]
{10.1093/mnrasl/slv047}, \href
{https://ui.adsabs.harvard.edu/abs/2015MNRAS.450L..61H} {450, L61}
\bibitem[\protect\citeauthoryear{{Handley}, {Hobson} \& {Lasenby}}{{Handley}
et~al.}{2015b}]{polychord2}
{Handley} W.~J., {Hobson} M.~P., {Lasenby} A.~N., 2015b, \mn@doi [\mnras]
{10.1093/mnras/stv1911}, \href
{https://ui.adsabs.harvard.edu/abs/2015MNRAS.453.4384H} {453, 4384}
\bibitem[\protect\citeauthoryear{{Handley}, {Lasenby}, {Peiris} \&
{Hobson}}{{Handley} et~al.}{2019}]{pkhandley}
{Handley} W.~J., {Lasenby} A.~N., {Peiris} H.~V., {Hobson} M.~P., 2019,
\mn@doi [\prd] {10.1103/PhysRevD.100.103511}, \href
{https://ui.adsabs.harvard.edu/abs/2019PhRvD.100j3511H} {100, 103511}
\bibitem[\protect\citeauthoryear{Harris et~al.,}{Harris et~al.}{2020}]{numpy}
Harris C.~R., et~al., 2020, \mn@doi [Nature] {10.1038/s41586-020-2649-2}, 585,
357
\bibitem[\protect\citeauthoryear{{Hee}, {Handley}, {Hobson} \&
{Lasenby}}{{Hee} et~al.}{2016}]{sonke}
{Hee} S., {Handley} W.~J., {Hobson} M.~P., {Lasenby} A.~N., 2016, \mn@doi
[\mnras] {10.1093/mnras/stv2217}, \href
{https://ui.adsabs.harvard.edu/abs/2016MNRAS.455.2461H} {455, 2461}
\bibitem[\protect\citeauthoryear{{Heimersheim}, {Sartorio}, {Fialkov} \&
{Lorimer}}{{Heimersheim} et~al.}{2022}]{heimersheimfrb}
{Heimersheim} S., {Sartorio} N.~S., {Fialkov} A., {Lorimer} D.~R., 2022,
\mn@doi [\apj] {10.3847/1538-4357/ac70c9}, \href
{https://ui.adsabs.harvard.edu/abs/2022ApJ...933...57H} {933, 57}
\bibitem[\protect\citeauthoryear{{Heimersheim}, {R{\o}nneberg}, {Linton},
{Pagani} \& {Fialkov}}{{Heimersheim} et~al.}{2024}]{heimersheim21cm}
{Heimersheim} S., {R{\o}nneberg} L., {Linton} H., {Pagani} F., {Fialkov}
A., 2024, \mn@doi [\mnras] {10.1093/mnras/stad3936}, \href
{https://ui.adsabs.harvard.edu/abs/2024MNRAS.52711404H} {527, 11404}
\bibitem[\protect\citeauthoryear{{Hergt}, {Handley}, {Hobson} \&
{Lasenby}}{{Hergt} et~al.}{2021}]{hergt}
{Hergt} L.~T., {Handley} W.~J., {Hobson} M.~P., {Lasenby} A.~N., 2021,
\mn@doi [\prd] {10.1103/PhysRevD.103.123511}, \href
{https://ui.adsabs.harvard.edu/abs/2021PhRvD.103l3511H} {103, 123511}
\bibitem[\protect\citeauthoryear{Hunter}{Hunter}{2007}]{matplotlib}
Hunter J.~D., 2007, \mn@doi [Computing in Science \& Engineering]
{10.1109/MCSE.2007.55}, 9, 90
\bibitem[\protect\citeauthoryear{{Johnson} \& {Jassal}}{{Johnson} \&
{Jassal}}{2025}]{2025arXiv250304273J}
{Johnson} J.~P., {Jassal} H.~K., 2025, \mn@doi [arXiv e-prints]
{10.48550/arXiv.2503.04273}, \href
{https://ui.adsabs.harvard.edu/abs/2025arXiv250304273J} {p. arXiv:2503.04273}
\bibitem[\protect\citeauthoryear{Li}{Li}{2023}]{smplotlib}
Li J., 2023, AstroJacobLi/smplotlib: v0.0.9, \mn@doi{10.5281/zenodo.8126529},
\url {https://doi.org/10.5281/zenodo.8126529}
\bibitem[\protect\citeauthoryear{{M}c{K}inney}{{M}c{K}inney}{2010}]{pandaspaper}
{M}c{K}inney W., 2010, in {S}t\'efan van~der {W}alt {J}arrod {M}illman eds,
{P}roceedings of the 9th {P}ython in {S}cience {C}onference. pp 56 -- 61,
\mn@doi{10.25080/Majora-92bf1922-00a}
\bibitem[\protect\citeauthoryear{{Millea} \& {Bouchet}}{{Millea} \&
{Bouchet}}{2018}]{flexknotreionization}
{Millea} M., {Bouchet} F., 2018, \mn@doi [\aap]
{10.1051/0004-6361/201833288}, \href
{https://ui.adsabs.harvard.edu/abs/2018A&A...617A..96M} {617, A96}
\bibitem[\protect\citeauthoryear{{Olamaie}, {Hobson}, {Feroz}, {Grainge},
{Lasenby}, {Perrott}, {Rumsey} \& {Saunders}}{{Olamaie}
et~al.}{2018}]{flexknotclusters}
{Olamaie} M., {Hobson} M.~P., {Feroz} F., {Grainge} K. J.~B., {Lasenby} A.,
{Perrott} Y.~C., {Rumsey} C., {Saunders} R. D.~E., 2018, \mn@doi
[\mnras] {10.1093/mnras/sty2495}, \href
{https://ui.adsabs.harvard.edu/abs/2018MNRAS.481.3853O} {481, 3853}
\bibitem[\protect\citeauthoryear{Ormondroyd}{Ormondroyd}{2025}]{ormondroyd_2025_15025604}
Ormondroyd A., 2025, {Nonparametric reconstructions of dynamical dark energy
using flexknots}, \mn@doi{10.5281/zenodo.15025604}, \url
{https://doi.org/10.5281/zenodo.15025604}
\bibitem[\protect\citeauthoryear{{Ormondroyd}, {Handley}, {Hobson} \&
{Lasenby}}{{Ormondroyd} et~al.}{2023}]{balancingact}
{Ormondroyd} A.~N., {Handley} W.~J., {Hobson} M.~P., {Lasenby} A.~N.,
2023, \mn@doi [arXiv e-prints] {10.48550/arXiv.2310.08490}, \href
{https://ui.adsabs.harvard.edu/abs/2023arXiv231008490O} {p. arXiv:2310.08490}
\bibitem[\protect\citeauthoryear{{Ormondroyd}, {Handley}, {Hobson} \&
{Lasenby}}{{Ormondroyd} et~al.}{2025}]{2025arXiv250308658O}
{Ormondroyd} A.~N., {Handley} W.~J., {Hobson} M.~P., {Lasenby} A.~N.,
2025, \mn@doi [arXiv e-prints] {10.48550/arXiv.2503.08658}, \href
{https://ui.adsabs.harvard.edu/abs/2025arXiv250308658O} {p. arXiv:2503.08658}
\bibitem[\protect\citeauthoryear{{Planck Collaboration} et~al.,}{{Planck
Collaboration} et~al.}{2014}]{pkplanck13}
{Planck Collaboration} et~al., 2014, \mn@doi [\aap]
{10.1051/0004-6361/201321569}, \href
{https://ui.adsabs.harvard.edu/abs/2014A&A...571A..22P} {571, A22}
\bibitem[\protect\citeauthoryear{{Planck Collaboration} et~al.,}{{Planck
Collaboration} et~al.}{2016}]{pkplanck15}
{Planck Collaboration} et~al., 2016, \mn@doi [\aap]
{10.1051/0004-6361/201525898}, \href
{https://ui.adsabs.harvard.edu/abs/2016A&A...594A..20P} {594, A20}
\bibitem[\protect\citeauthoryear{{Shen}, {Anstey}, {de Lera Acedo} \&
{Fialkov}}{{Shen} et~al.}{2024}]{shen}
{Shen} E., {Anstey} D., {de Lera Acedo} E., {Fialkov} A., 2024, \mn@doi
[\mnras] {10.1093/mnras/stae614}, \href
{https://ui.adsabs.harvard.edu/abs/2024MNRAS.529.1642S} {529, 1642}
\bibitem[\protect\citeauthoryear{{Skilling}}{{Skilling}}{2004}]{skilling2004}
{Skilling} J., 2004, in {Fischer} R., {Preuss} R., {Toussaint} U.~V., eds,
American Institute of Physics Conference Series Vol. 735, Bayesian Inference
and Maximum Entropy Methods in Science and Engineering: 24th International
Workshop on Bayesian Inference and Maximum Entropy Methods in Science and
Engineering. pp 395--405, \mn@doi{10.1063/1.1835238}
\bibitem[\protect\citeauthoryear{{The pandas development team}}{{The pandas
development team}}{2023}]{pandaszenodo}
{The pandas development team} 2023, pandas-dev/pandas: Pandas,
\mn@doi{10.5281/zenodo.8092754}, \url
{https://doi.org/10.5281/zenodo.8092754}
\bibitem[\protect\citeauthoryear{{V{\'a}zquez}, {Bridges}, {Hobson} \&
{Lasenby}}{{V{\'a}zquez} et~al.}{2012a}]{pkvazquez}
{V{\'a}zquez} J.~A., {Bridges} M., {Hobson} M.~P., {Lasenby} A.~N., 2012a,
\mn@doi [\jcap] {10.1088/1475-7516/2012/06/006}, \href
{https://ui.adsabs.harvard.edu/abs/2012JCAP...06..006V} {2012, 006}
\bibitem[\protect\citeauthoryear{{V{\'a}zquez}, {Bridges}, {Hobson} \&
{Lasenby}}{{V{\'a}zquez} et~al.}{2012b}]{devazquez}
{V{\'a}zquez} J.~A., {Bridges} M., {Hobson} M.~P., {Lasenby} A.~N., 2012b,
\mn@doi [\jcap] {10.1088/1475-7516/2012/09/020}, \href
{https://ui.adsabs.harvard.edu/abs/2012JCAP...09..020V} {2012, 020}
\bibitem[\protect\citeauthoryear{Virtanen et~al.,}{Virtanen
et~al.}{2020}]{scipy}
Virtanen P., et~al., 2020, \mn@doi [Nature Methods]
{10.1038/s41592-019-0686-2}, \href {https://rdcu.be/b08Wh} {17, 261}
\bibitem[\protect\citeauthoryear{{Yang}, {Wang}, {Li}, {Yuan}, {Ren},
{Saridakis} \& {Cai}}{{Yang} et~al.}{2025}]{quintom}
{Yang} Y., {Wang} Q., {Li} C., {Yuan} P., {Ren} X., {Saridakis} E.~N.,
{Cai} Y.-F., 2025, \mn@doi [arXiv e-prints] {10.48550/arXiv.2501.18336},
\href {https://ui.adsabs.harvard.edu/abs/2025arXiv250118336Y} {p.
arXiv:2501.18336}
\makeatother
\end{thebibliography}
```
5. **Author Information:**
- Lead Author: {'name': 'A. N. Ormondroyd'}
- Full Authors List:
```yaml
Adam Ormondroyd:
phd:
start: 2021-10-01
supervisors:
- Mike Hobson
- Will Handley
- Anthony Lasenby
thesis: null
original_image: images/originals/adam_ormondroyd.jpg
image: /assets/group/images/adam_ormondroyd.jpg
links:
linkedin: https://www.linkedin.com/in/adam-ormondroyd/
GitHub: https://github.com/AdamOrmondroyd
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
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
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
```
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 [2503.17342](https://arxiv.org/abs/2503.17342) is featured in the first sentence.
Generate only the final Markdown output that meets all these requirements.
{% endraw %}