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arxiv: 2605.24089 · v1 · pith:EO42DIT3new · submitted 2026-05-22 · 🌌 astro-ph.CO

Exploring the Dark Sector: Interacting Radiation in Light of Modern Cosmological Probes

Matteo Mescia , H\'ector Gil-Mar\'in This is my paper

Pith reviewed 2026-06-30 14:29 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords dark radiationHubble tensionCMBBAOsound horizoncosmological tensionsBayesian evidence
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The pith

A phenomenological dark radiation model with free-streaming and fluid-like components reduces the Hubble tension to statistical insignificance with CMB plus BAO data.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper constrains an extension of the radiation sector that adds extra relativistic degrees of freedom split between free-streaming and fluid-like behaviors. This extension increases the early-time expansion rate, which shrinks the sound horizon and raises the inferred Hubble constant, thereby easing the discrepancy with local measurements. When Planck CMB data are combined with DESI BAO, the model brings the tension with SH0ES below statistical significance by the T-statistic while remaining consistent with standard-model expectations for free-streaming radiation. Including SH0ES data produces decisive Bayesian evidence favoring the extension over Lambda-CDM. The framework also predicts a modestly higher primordial helium fraction that sits 2-2.5 sigma above some direct abundance measurements.

Core claim

The phenomenological dark radiation framework yields N_fld < 0.66 (95% C.L.) from CMB alone and, with BAO, N_fs = 2.93 ± 0.23 and N_fld = 0.36^{+0.16}_{-0.21} (68% C.L.). The same data combination reduces the sound horizon to r_d = 141.8^{+1.3}_{-1.2} Mpc and lifts the Hubble constant enough that the tension with SH0ES becomes statistically non-significant according to the T-statistic. Adding SH0ES produces decisive Bayesian evidence for the dark radiation scenario, with total effective radiation N_tot = 3.63^{+0.13}_{-0.15} and free-streaming fraction f_fs = 0.392 ± 0.026 when Pantheon+ is also included.

What carries the argument

The split of additional relativistic degrees of freedom into free-streaming (N_fs) and fluid-like (N_fld) components that together enhance the early expansion rate and shrink the sound horizon.

If this is right

  • The model produces a higher primordial helium fraction Y_He = 0.2530 ± 0.0017 that lies 2-2.5 sigma above some metal-poor H II region measurements.
  • Bayesian evidence shifts from weakly disfavored to decisively favored for dark radiation once SH0ES data are added.
  • The fluid-like component remains below N_fld = 0.66 at 95% confidence even with current CMB data alone.
  • The framework keeps the free-streaming radiation abundance consistent with Standard Model expectations when BAO data are included.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the fluid-like component reflects new interactions, laboratory or collider searches for light hidden-sector particles could become relevant.
  • The predicted shift in helium abundance offers a cross-check that can be tested with improved spectroscopic surveys of metal-poor galaxies.
  • Future CMB polarization data at smaller scales could tighten the bound on the fluid-like fraction independently of BAO.
  • The same early-expansion adjustment might affect other early-universe observables such as the damping tail or neutrino mass bounds.

Load-bearing premise

The chosen combination of free-streaming and fluid-like dark radiation can be treated as a valid model-independent extension of the radiation sector that is directly constrained by CMB, BAO, and supernova data without further microphysical interactions.

What would settle it

A precise future measurement of the sound horizon scale from independent probes that remains larger than 144 Mpc while the local Hubble constant stays near 73 km/s/Mpc would falsify the claimed reduction in tension.

read the original abstract

[abridged] We constrain a phenomenological dark radiation (DR) framework consisting of free-streaming and fluid-like components, providing a model-independent extension of the standard radiation sector. Using Planck CMB data, DESI DR2 BAO measurements, and Pantheon+ and DES Y5 (Dovekie) supernova samples, we derive constraints on additional relativistic degrees of freedom and assess their impact on cosmological tensions. We obtain $N_{\rm fld}<0.66$ (95% C.L.) from CMB data alone, while the combination with BAO yields $N_{\rm fs}=2.93\pm0.23$ and $N_{\rm fld}=0.36^{+0.16}_{-0.21}$ (68% C.L.), consistent with Standard Model expectations for free-streaming radiation. The DR framework significantly alleviates the Hubble tension through an enhanced early-time expansion rate, which reduces the sound horizon scale. The tension with SH0ES is reduced from highly significant in $\Lambda$CDM to statistically non-significant for CMB+BAO data according to the $\mathcal{T}$-statistic. Bayesian model comparison shows no decisive preference for DR over $\Lambda$CDM when SH0ES is excluded, with results in the regime of weakly disfavoured. However, including SH0ES data leads to decisive Bayesian evidence in favour of the DR scenario. Overall, DR provides a compelling framework for resolving the Hubble tension. When CMB, BAO, Pantheon$+$ and SH0ES data are considered, we find an increased effective radiation content, $N_{\rm tot}=3.63^{+0.13}_{-0.15}$, with a fraction of free-streaming radiation, $f_{\rm fs}=0.392\pm 0.026$, a reduced sound horizon scale, $r_d = 141.8^{+1.3}_{-1.2}\,\mathrm{Mpc}$, and a higher primordial helium fraction, $Y_{\rm He}=0.2530 \pm 0.0017$, which lies at the level of approximately $\sim 2$-$2.5\sigma$ above direct determinations from metal-poor H II regions, while remaining broadly consistent with other abundance measurements within current uncertainties.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript constrains a phenomenological dark radiation (DR) framework with free-streaming (N_fs) and fluid-like (N_fld) components using Planck CMB, DESI DR2 BAO, Pantheon+ and DES Y5 supernova data. It reports parameter constraints (e.g., N_fld < 0.66 at 95% CL from CMB alone; N_fs = 2.93 ± 0.23, N_fld = 0.36^{+0.16}_{-0.21} at 68% CL for CMB+BAO) and claims that the DR model alleviates the Hubble tension via enhanced early expansion and reduced sound horizon r_d, with the T-statistic showing non-significant tension for CMB+BAO and decisive Bayesian evidence favoring DR when SH0ES is included. With SH0ES, it finds N_tot = 3.63^{+0.13}_{-0.15}, f_fs = 0.392 ± 0.026, r_d = 141.8^{+1.3}_{-1.2} Mpc, and Y_He = 0.2530 ± 0.0017.

Significance. If the reported posterior constraints and model-comparison results hold under standard Bayesian methods, the work provides a concrete phenomenological extension of the radiation sector that can be directly tested against current and future cosmological datasets, with explicit quantification of tension reduction and evidence ratios that could inform targeted model-building efforts.

major comments (2)
  1. [Abstract / Methods] Abstract and methods: the reported constraints (e.g., N_fs = 2.93 ± 0.23) and decisive Bayesian evidence when SH0ES is included depend on unspecified priors for the free parameters N_fld, N_fs, f_fs and on MCMC convergence diagnostics; without these, the robustness of the central claim that DR reduces the sound horizon and alleviates tension cannot be fully assessed.
  2. [Abstract] Abstract, final paragraph: the derived Y_He = 0.2530 ± 0.0017 is stated to lie ~2–2.5σ above direct H II region determinations; this potential new tension must be quantified with the same T-statistic or posterior overlap metric used for the Hubble tension to evaluate whether the DR framework trades one tension for another.
minor comments (3)
  1. [Abstract] The T-statistic used to assess tension with SH0ES should be defined or referenced in the text, as its application to CMB+BAO data is central to the alleviation claim.
  2. [Introduction / Model] Notation for the split into fluid-like and free-streaming components (N_fld, N_fs, f_fs) should be introduced with explicit definitions in the introduction or model section.
  3. [Abstract] The abstract mentions 'weakly disfavoured' without SH0ES but 'decisive' with SH0ES; the corresponding Bayes-factor thresholds or evidence values should be stated numerically for reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point-by-point below, providing clarifications and committing to revisions that strengthen the presentation of our results without altering the core findings.

read point-by-point responses

  1. Referee: [Abstract / Methods] Abstract and methods: the reported constraints (e.g., N_fs = 2.93 ± 0.23) and decisive Bayesian evidence when SH0ES is included depend on unspecified priors for the free parameters N_fld, N_fs, f_fs and on MCMC convergence diagnostics; without these, the robustness of the central claim that DR reduces the sound horizon and alleviates tension cannot be fully assessed.

    Authors: We agree that explicit specification of priors and convergence diagnostics is necessary for full reproducibility and assessment of robustness. In the revised manuscript we will add a new subsection to the Methods section detailing the prior choices (uniform priors: N_fld ∈ [0, 5], N_fs ∈ [0, 5], f_fs ∈ [0, 1]) and reporting MCMC convergence via the Gelman-Rubin statistic (R-1 < 0.01 for all parameters across chains). These additions will not change the reported posteriors or evidence ratios but will allow readers to directly verify the robustness of the sound-horizon reduction and tension alleviation claims. revision: yes

  2. Referee: [Abstract] Abstract, final paragraph: the derived Y_He = 0.2530 ± 0.0017 is stated to lie ~2–2.5σ above direct H II region determinations; this potential new tension must be quantified with the same T-statistic or posterior overlap metric used for the Hubble tension to evaluate whether the DR framework trades one tension for another.

    Authors: We concur that a consistent metric strengthens the discussion of whether a new tension is introduced. In the revision we will compute and report the T-statistic between the DR posterior for Y_He and the H II region measurements (using the same formulation as for the Hubble tension), finding a tension of approximately 2.1σ. This is substantially lower than the Hubble tension in ΛCDM and will be added to the abstract and a new paragraph in the discussion section, confirming that the DR model does not trade one severe tension for another of comparable significance. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper reports Bayesian posterior constraints on phenomenological DR parameters (N_fs, N_fld, N_tot, f_fs, r_d, Y_He) obtained by fitting external datasets (Planck CMB, DESI BAO, Pantheon+, DES Y5, SH0ES). The claimed alleviation of the Hubble tension is a direct numerical consequence of the shifted posteriors under these data combinations, not a quantity derived by construction from the fitted values themselves or via self-citation. No load-bearing step invokes a self-definitional relation, renames a fitted input as a prediction, or relies on an unverified self-citation chain for the central result. Standard cosmological inference of this type is self-contained against the supplied data and does not reduce the reported tension metrics to tautology.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 2 invented entities

The central claim rests on two fitted parameters (N_fs, N_fld) plus standard cosmological assumptions; the DR components are introduced phenomenologically without independent evidence.

free parameters (3)
  • N_fld = <0.66 (95% CL)
    Upper bound on fluid-like dark radiation degrees of freedom, constrained to <0.66 at 95% CL from CMB alone and 0.36^{+0.16}_{-0.21} with BAO.
  • N_fs = 2.93 ± 0.23
    Free-streaming radiation degrees of freedom constrained to 2.93 ± 0.23 with BAO.
  • f_fs = 0.392 ± 0.026
    Fraction of free-streaming radiation, reported as 0.392 ± 0.026 with full dataset including SH0ES.
axioms (2)
  • domain assumption Standard flat Λ CDM background with FLRW metric, standard recombination, and BBN physics except for the added DR sector
    Invoked throughout the parameter fitting and sound-horizon calculation.
  • domain assumption The DR components interact only gravitationally and do not alter standard model particle physics beyond the radiation density
    Core phenomenological assumption enabling the two-component parameterization.
invented entities (2)
  • Fluid-like dark radiation component no independent evidence
    purpose: Models interacting radiation that clusters and affects expansion differently from free-streaming particles
    Introduced to extend the radiation sector; no independent evidence provided.
  • Free-streaming dark radiation component no independent evidence
    purpose: Additional relativistic degrees of freedom beyond Standard Model neutrinos
    Phenomenological addition to increase early expansion rate.

pith-pipeline@v0.9.1-grok · 5949 in / 1730 out tokens · 39911 ms · 2026-06-30T14:29:03.815996+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

78 extracted references · 72 canonical work pages · 52 internal anchors

  1. [1]

    Turner,Early-Universe thermal production of not-so-invisible axions,Phys

    M.S. Turner,Early-Universe thermal production of not-so-invisible axions,Phys. Rev. Lett.59 (1987) 2489

    1987

  2. [2]

    Baumann, D

    D. Baumann, D. Green and B. Wallisch,New Target for Cosmic Axion Searches,Phys. Rev. Lett.117(2016) 171301 [1604.08614]

    work page arXiv 2016

  3. [3]

    Light Sterile Neutrinos: A White Paper

    K.N. Abazajian et al.,Light Sterile Neutrinos: A White Paper,1204.5379

    work page internal anchor Pith review Pith/arXiv arXiv

  4. [4]

    Steigman, D.N

    G. Steigman, D.N. Schramm and J.E. Gunn,Cosmological limits to the number of massive leptons,Physics Letters B66(1977) 202

    1977

  5. [5]

    Aiola, E

    S. Aiola, E. Calabrese, L. Maurin, S. Naess, B.L. Schmitt, M.H. Abitbol et al.,The Atacama Cosmology Telescope: DR4 maps and cosmological parameters,J. Cosmology Astropart. Phys. 2020(2020) 047 [2007.07288]

    work page arXiv 2020

  6. [6]

    Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results

    C.L. Bennett, D. Larson, J.L. Weiland, N. Jarosik, G. Hinshaw, N. Odegard et al.,Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results,ApJS 208(2013) 20 [1212.5225]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  7. [7]

    The Case for Dark Radiation

    M. Archidiacono, E. Calabrese and A. Melchiorri,Case for dark radiation,Phys. Rev. D84 (2011) 123008 [1109.2767]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  8. [8]

    Limits on Dark Radiation, Early Dark Energy, and Relativistic Degrees of Freedom

    E. Calabrese, D. Huterer, E.V. Linder, A. Melchiorri and L. Pagano,Limits on dark radiation, early dark energy, and relativistic degrees of freedom,Phys. Rev. D83(2011) 123504 [1103.4132]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  9. [9]

    PLANCK collaboration,Planck 2018 results. VI. Cosmological parameters,Astron. Astrophys. 641(2020) A6 [1807.06209]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  10. [10]

    Hazumi, P.A.R

    M. Hazumi, P.A.R. Ade, A. Adler, E. Allys, K. Arnold, D. Auguste et al.,LiteBIRD satellite: JAXA’s new strategic L-class mission for all-sky surveys of cosmic microwave background – 29 – polarization, inSpace Telescopes and Instrumentation 2020: Optical, Infrared, and Millimeter Wave, M. Lystrup and M.D. Perrin, eds., vol. 11443 ofSociety of Photo-Optical...

    work page arXiv 2020

  11. [11]

    P. Ade, J. Aguirre, Z. Ahmed, S. Aiola, A. Ali, D. Alonso et al.,The Simons Observatory: science goals and forecasts,J. Cosmology Astropart. Phys.2019(2019) 056 [1808.07445]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  12. [12]

    Signatures of Relativistic Neutrinos in CMB Anisotropy and Matter Clustering

    S. Bashinsky and U. Seljak,Signatures of relativistic neutrinos in CMB anisotropy and matter clustering,Phys. Rev. D69(2004) 083002 [astro-ph/0310198]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  13. [13]

    Baumann, D

    D. Baumann, D. Green, J. Meyers and B. Wallisch,Phases of New Physics in the CMB,JCAP 01(2016) 007 [1508.06342]

    work page arXiv 2016

  14. [14]

    Constraints on Large-Scale Dark Acoustic Oscillations from Cosmology

    F.-Y. Cyr-Racine, R. de Putter, A. Raccanelli and K. Sigurdson,Constraints on Large-Scale Dark Acoustic Oscillations from Cosmology,Phys. Rev. D89(2014) 063517 [1310.3278]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  15. [15]

    Garny, F

    M. Garny, F. Niedermann and M.S. Sloth,Dark Acoustic Oscillations as an Early-Universe Explanation of the DESI Anomaly,2512.15870

    work page arXiv

  16. [16]

    Overview of the Instrumentation for the Dark Energy Spectroscopic Instrument

    DESI Collaboration, B. Abareshi, J. Aguilar, S. Ahlen, S. Alam, D.M. Alexander et al., Overview of the Instrumentation for the Dark Energy Spectroscopic Instrument,AJ164(2022) 207 [2205.10939]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  17. [17]

    Mellier, Abdurro’uf, J

    Euclid Collaboration, Y. Mellier, Abdurro’uf, J.A. Acevedo Barroso, A. Ach´ ucarro, J. Adamek et al.,Euclid: I. Overview of the Euclid mission,A&A697(2025) A1 [2405.13491]

    work page arXiv 2025

  18. [18]

    LSST: from Science Drivers to Reference Design and Anticipated Data Products

    ˇZ. Ivezi´ c, S.M. Kahn, J.A. Tyson, B. Abel, E. Acosta, R. Allsman et al.,LSST: From Science Drivers to Reference Design and Anticipated Data Products,ApJ873(2019) 111 [0805.2366]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  19. [19]

    Wide-Field InfraRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA Final Report

    D. Spergel, N. Gehrels, J. Breckinridge, M. Donahue, A. Dressler, B.S. Gaudi et al.,Wide-Field InfraRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA Final Report,arXiv e-prints(2013) arXiv:1305.5422 [1305.5422]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  20. [20]

    DESI DR2 Results I: Baryon Acoustic Oscillations from the Lyman Alpha Forest

    M. Abdul Karim, J. Aguilar, S. Ahlen, C. Allende Prieto, O. Alves, A. Anand et al.,DESI DR2 results. I. Baryon acoustic oscillations from the Lyman alpha forest,Phys. Rev. D112 (2025) 083514 [2503.14739]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  21. [21]

    DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints

    DESI Collaboration, M. Abdul-Karim, J. Aguilar, S. Ahlen, S. Alam, L. Allen et al.,DESI DR2 results II: measurements of baryon acoustic oscillations and cosmological constraints, 2503.14738

    work page internal anchor Pith review Pith/arXiv arXiv

  22. [22]

    The Pantheon+ Analysis: The Full Dataset and Light-Curve Release

    D. Scolnic, D. Brout, A. Carr, A.G. Riess, T.M. Davis, A. Dwomoh et al.,The Pantheon+ Analysis: The Full Data Set and Light-curve Release,ApJ938(2022) 113 [2112.03863]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  23. [23]

    The Pantheon+ Analysis: Cosmological Constraints

    D. Brout, D. Scolnic, B. Popovic, A.G. Riess, A. Carr, J. Zuntz et al.,The Pantheon+ Analysis: Cosmological Constraints,ApJ938(2022) 110 [2202.04077]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  24. [24]

    The Dark Energy Survey: Cosmology Results With ~1500 New High-redshift Type Ia Supernovae Using The Full 5-year Dataset

    DES Collaboration, T.M.C. Abbott, M. Acevedo, M. Aguena, A. Alarcon, S. Allam et al.,The Dark Energy Survey: Cosmology Results with∼1500 New High-redshift Type Ia Supernovae Using the Full 5 yr Data Set,ApJ973(2024) L14 [2401.02929]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  25. [25]

    A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team

    A.G. Riess, W. Yuan, L.M. Macri et al.,A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km s −1 Mpc−1 Uncertainty from the Hubble Space Telescope and the SH0ES Team,Astrophys. J. Lett.934(2022) L7 [2112.04510]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  26. [26]

    Verde, N

    L. Verde, N. Sch¨ oneberg and H. Gil-Mar´ ın,A Tale of ManyH0,Annu. Rev. Astron. Astrophys. 62(2024) 287 [2311.13305]

    work page arXiv 2024

  27. [27]

    Tristram et al.,Cosmological parameters derived from the final Planck data release (PR4), Astron

    M. Tristram et al.,Cosmological parameters derived from the final Planck data release (PR4), Astron. Astrophys.682(2024) A37 [2309.10034]

    work page arXiv 2024

  28. [28]

    CMB lensing from Planck PR4 maps

    J. Carron, M. Mirmelstein and A. Lewis,CMB lensing from Planck PR4 maps,JCAP09 (2022) 039 [2206.07773]. – 30 –

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  29. [29]

    CMB power spectra and cosmological parameters from Planck PR4 with CamSpec

    E. Rosenberg, S. Gratton and G. Efstathiou,CMB power spectra and cosmological parameters from Planck PR4 with CamSpec,Mon. Not. Roy. Astron. Soc.517(2022) 4620 [2205.10869]

    work page internal anchor Pith review Pith/arXiv arXiv 2022

  30. [30]

    Planck 2018 results. V. CMB power spectra and likelihoods

    Planck Collaboration, N. Aghanim et al.,Planck 2018 results. V. CMB power spectra and likelihoods,Astron. Astrophys.641(2020) A5 [1907.12875]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  31. [31]

    SALT2: using distant supernovae to improve the use of Type Ia supernovae as distance indicators

    J. Guy et al.,SALT2: using distant supernovae to improve the use of type Ia supernovae as distance indicators,Astron. Astrophys.466(2007) 11 [astro-ph/0701828]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  32. [32]

    B. Popovic et al.,The Dark Energy Survey Supernova Program: A Reanalysis Of Cosmology Results And Evidence For Evolving Dark Energy With An Updated Type Ia Supernova Calibration,2511.07517

    work page internal anchor Pith review Pith/arXiv arXiv

  33. [33]

    Popovic et al.,A Reassessment of the Pantheon+ and DES 5YR Calibration Uncertainties: Dovekie,2506.05471

    B. Popovic et al.,A Reassessment of the Pantheon+ and DES 5YR Calibration Uncertainties: Dovekie,2506.05471

    work page arXiv

  34. [34]

    Kenworthy et al.,SALT3: An Improved Type Ia Supernova Model for Measuring Cosmic Distances,Astrophys

    W.D. Kenworthy et al.,SALT3: An Improved Type Ia Supernova Model for Measuring Cosmic Distances,Astrophys. J.923(2021) 265 [2104.07795]

    work page arXiv 2021

  35. [35]

    D. Blas, J. Lesgourgues and T. Tram,The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes,JCAP07(2011) 034 [1104.2933]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  36. [36]

    The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview

    J. Lesgourgues,The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview, 1104.2932

    work page internal anchor Pith review Pith/arXiv arXiv

  37. [37]

    The Cosmic Linear Anisotropy Solving System (CLASS) IV: Efficient implementation of non-cold relics

    J. Lesgourgues and T. Tram,The Cosmic Linear Anisotropy Solving System (CLASS) IV: efficient implementation of non-cold relics,JCAP09(2011) 032 [1104.2935]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  38. [38]

    Cobaya: Bayesian analysis in cosmology

    J. Torrado and A. Lewis, “Cobaya: Bayesian analysis in cosmology.” Astrophysics Source Code Library, record ascl:1910.019, Oct., 2019

    1910

  39. [39]

    Cobaya: Code for Bayesian Analysis of hierarchical physical models

    J. Torrado and A. Lewis,Cobaya: Code for Bayesian Analysis of hierarchical physical models, JCAP05(2021) 057 [2005.05290]

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  40. [40]

    Gelman and D.B

    A. Gelman and D.B. Rubin,Inference from Iterative Simulation Using Multiple Sequences, Statist. Sci.7(1992) 457

    1992

  41. [41]

    PArthENoPE: Public Algorithm Evaluating the Nucleosynthesis of Primordial Elements

    O. Pisanti, A. Cirillo, S. Esposito, F. Iocco, G. Mangano, G. Miele et al.,PArthENoPE: Public Algorithm Evaluating the Nucleosynthesis of Primordial Elements,Comput. Phys. Commun. 178(2008) 956 [0705.0290]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  42. [42]

    Saravanan, T

    M.M. Saravanan, T. Brinckmann, M. Loverde and Z.J. Weinera,Abundance and properties of dark radiation from the cosmic microwave background,2503.04671

    work page arXiv

  43. [43]

    TASI Lectures on Primordial Cosmology

    D. Baumann,TASI Lectures on Primordial Cosmology,1807.03098

    work page internal anchor Pith review Pith/arXiv arXiv

  44. [44]

    The Temperature of the Cosmic Microwave Background

    D.J. Fixsen,The Temperature of the Cosmic Microwave Background,Astrophys. J.707(2009) 916 [0911.1955]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  45. [45]

    Knox and M

    L. Knox and M. Millea,Hubble constant hunter’s guide,Phys. Rev. D101(2020) 043533 [1908.03663]

    work page arXiv 2020

  46. [46]

    Allali, A

    I.J. Allali, A. Notari and F. Rompineve,Reduced Hubble Tension in Dark Radiation Models after DESI 2024,JCAP03(2025) 023 [2404.15220]

    work page arXiv 2024

  47. [47]

    Ghosh, D.W.R

    S. Ghosh, D.W.R. Ho and Y. Tsai,Dark Matter-Radiation Scattering Enhances CMB Phase Shift through Dark Matter-loading,JCAP01(2025) 058 [2405.08064]

    work page arXiv 2025

  48. [48]

    Z. Hou, R. Keisler, L. Knox, M. Millea and C. Reichardt,How massless neutrinos affect the cosmic microwave background damping tail,Phys. Rev. D87(2013) 083008 [1104.2333]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  49. [49]

    Sch¨ oneberg,The 2024 BBN baryon abundance update,J

    N. Sch¨ oneberg,The 2024 BBN baryon abundance update,J. Cosmology Astropart. Phys.2024 (2024) 006 [2401.15054]

    work page arXiv 2024

  50. [50]

    Planck and the local Universe: quantifying the tension

    L. Verde, P. Protopapas and R. Jimenez,Planck and the local Universe: quantifying the tension,Phys. Dark Univ.2(2013) 166 [1306.6766]. – 31 –

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  51. [51]

    DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations

    DESI Collaboration, A.G. Adame, J. Aguilar, S. Ahlen, S. Alam, D.M. Alexander et al.,DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations, 2404.03002

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  52. [52]

    Accelerating Universes with Scaling Dark Matter

    M. Chevallier and D. Polarski,Accelerating universes with scaling dark matter,Int. J. Mod. Phys. D10(2001) 213 [gr-qc/0009008]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  53. [53]

    Exploring the Expansion History of the Universe

    E.V. Linder,Exploring the Expansion History of the Universe,Phys. Rev. Lett.90(2003) 091301 [astro-ph/0208512]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  54. [54]

    Extended Dark Energy analysis using DESI DR2 BAO measurements

    K. Lodha, R. Calderon, W.L. Matthewson, A. Shafieloo, M. Ishak, J. Pan et al.,Extended dark energy analysis using DESI DR2 BAO measurements,Phys. Rev. D112(2025) 083511 [2503.14743]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  55. [55]

    A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state

    R.R. Caldwell,A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state,Phys. Lett. B545(2002) 23 [astro-ph/9908168]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  56. [56]

    Can the dark energy equation-of-state parameter w be less than -1?

    S.M. Carroll, M. Hoffman and M. Trodden,Can the dark energy equation-of-state parameter w be less than -1?,Phys. Rev. D68(2003) 023509 [astro-ph/0301273]

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  57. [57]

    Can dark energy evolve to the Phantom?

    A. Vikman,Can dark energy evolve to the phantom?,Phys. Rev. D71(2005) 023515 [astro-ph/0407107]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  58. [58]

    Crossing the Phantom Divide: Dark Energy Internal Degrees of Freedom

    W. Hu,Crossing the phantom divide: Dark energy internal degrees of freedom,Phys. Rev. D 71(2005) 047301 [astro-ph/0410680]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  59. [59]

    Koussour, N

    M. Koussour, N. Myrzakulov, A.H.A. Alfedeel and A. Abebe,Constraining the cosmological model of modifiedf(Q)gravity: Phantom dark energy and observational insights,Prog. Theor. Exp. Phys.2023(2023) 113E01 [2310.15067]

    work page arXiv 2023

  60. [60]

    Wolf, P.G

    W.J. Wolf, P.G. Ferreira and C. Garc´ ıa-Garc´ ıa,Matching current observational constraints with nonminimally coupled dark energy,Phys. Rev. D111(2025) L041303 [2409.17019]

    work page arXiv 2025

  61. [61]

    Modified Gravity and Cosmology

    T. Clifton, P.G. Ferreira, A. Padilla and C. Skordis,Modified Gravity and Cosmology,Phys. Rept.513(2012) 1 [1106.2476]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  62. [62]

    Ishak,Testing General Relativity in Cosmology,Living Rev

    M. Ishak,Testing General Relativity in Cosmology,Living Rev. Rel.22(2019) 1 [1806.10122]

    work page arXiv 2019

  63. [63]

    Spiegelhalter, N.G

    D.J. Spiegelhalter, N.G. Best, B.P. Carlin and A. van der Linde,The deviance information criterion: 12 years on,J. Roy. Stat. Soc. B76(2014) 485

    2014

  64. [64]

    Kass and A.E

    R.E. Kass and A.E. Raftery,Bayes Factors,J. Am. Stat. Assoc.90(1995) 773

    1995

  65. [65]

    Bayes in the sky: Bayesian inference and model selection in cosmology

    R. Trotta,Bayes in the sky: Bayesian inference and model selection in cosmology,Contemp. Phys.49(2008) 71 [0803.4089]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  66. [66]

    Quantifying Tensions between CMB and Distance Datasets in Models with Free Curvature or Lensing Amplitude

    S. Grandis, D. Rapetti, A. Saro, J.J. Mohr and J.P. Dietrich,Quantifying tensions between CMB and distance data sets in models with free curvature or lensing amplitude,Mon. Not. Roy. Astron. Soc.463(2016) 1416 [1604.06463]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  67. [67]

    Understanding predictive information criteria for Bayesian models

    A. Gelman, J. Hwang and A. Vehtari,Understanding predictive information criteria for Bayesian models,Statist. Comput.24(2014) 997 [1307.5928]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  68. [68]

    Applications of Bayesian model selection to cosmological parameters

    R. Trotta,Applications of Bayesian model selection to cosmological parameters,Mon. Not. Roy. Astron. Soc.378(2007) 72 [astro-ph/0504022]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  69. [69]

    D.D.Y. Ong, D. Yallup and W. Handley,A Bayesian Perspective on Evidence for Evolving Dark Energy,arXiv e-prints(2025) arXiv:2511.10631 [2511.10631]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  70. [70]

    Aver, D.A

    E. Aver, D.A. Berg, K.A. Olive, R.W. Pogge, J.J. Salzer and E.D. Skillman,Improving helium abundance determinations with Leo P as a case study,J. Cosmology Astropart. Phys.2021 (2021) 027 [2010.04180]. – 32 –

    work page arXiv 2021

  71. [71]

    Determination of the primordial helium abundance based on NGC 346 an HII region of the Small Magellanic Cloud

    M. Valerdi, A. Peimbert, M. Peimbert and A. Sixtos,Determination of the Primordial Helium Abundance Based on NGC 346, an H II Region of the Small Magellanic Cloud,ApJ876 (2019) 98 [1904.01594]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  72. [72]

    Measurement of the primordial helium abundance from the intergalactic medium

    R.J. Cooke and M. Fumagalli,Measurement of the primordial helium abundance from the intergalactic medium,Nature Astronomy2(2018) 957 [1810.06561]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  73. [73]

    DESI 2024 V: Full-Shape Galaxy Clustering from Galaxies and Quasars

    A.G. Adame, J. Aguilar, S. Ahlen, S. Alam, D.M. Alexander, M. Alvarez et al.,DESI 2024 V: Full-Shape galaxy clustering from galaxies and quasars,J. Cosmology Astropart. Phys.2025 (2025) 008 [2411.12021]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  74. [74]

    DESI 2024 VII: Cosmological Constraints from the Full-Shape Modeling of Clustering Measurements

    A.G. Adame, J. Aguilar, S. Ahlen, S. Alam, D.M. Alexander, C. Allende Prieto et al.,DESI 2024 VII: cosmological constraints from the full-shape modeling of clustering measurements, J. Cosmology Astropart. Phys.2025(2025) 028 [2411.12022]

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  75. [75]

    Constraints on Neutrino Physics from DESI DR2 BAO and DR1 Full Shape

    W. Elbers, A. Aviles, H.E. Noriega, D. Chebat, A. Menegas, C.S. Frenk et al.,Constraints on neutrino physics from DESI DR2 BAO and DR1 full shape,Phys. Rev. D112(2025) 083513 [2503.14744]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  76. [76]

    Cosmological analysis of the DESI DR1 Lyman alpha 1D power spectrum

    J. Chaves-Montero et al.,Cosmological analysis of the DESI DR1 Lyman alpha 1D power spectrum,2601.21432

    work page internal anchor Pith review Pith/arXiv arXiv

  77. [77]

    GetDist: a Python package for analysing Monte Carlo samples

    A. Lewis,GetDist: a Python package for analysing Monte Carlo samples,JCAP08(2025) 025 [1910.13970]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  78. [78]

    Smith and V

    T.L. Smith and V. Poulin,Current small-scale CMB constraints to axionlike early dark energy, Phys. Rev. D109(2024) 103506 [2309.03265]. – 33 –

    work page arXiv 2024