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arxiv: 2512.11041 · v2 · submitted 2025-12-11 · 🌌 astro-ph.CO

KiDS-Legacy: Constraining dark energy, neutrino mass, and curvature

Robert Reischke , Benjamin St\"olzner , Benjamin Joachimi , Angus H. Wright , Marika Asgari , Maciej Bilicki , Nora Elisa Chisari , Andrej Dvornik
show 20 more authors
Christos Georgiou Benjamin Giblin Joachim Harnois-D\'eraps Catherine Heymans Hendrik Hildebrandt Henk Hoekstra Shahab Joudaki Konrad Kuijken Shun-Sheng Li Laila Linke Arthur Loureiro Constance Mahony Lauro Moscardini Lucas Porth Mario Radovich Tilman Tr\"oster Maximilian von Wietersheim-Kramsta Ziang Yan Mijin Yoon Yun-Hao Zhang
This is my paper

Pith reviewed 2026-05-16 22:48 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords KiDScosmic sheardark energyneutrino massspatial curvatureLambda-CDMS8cosmological constraints
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The pith

KiDS-Legacy cosmic shear data aligns with flat Lambda-CDM, producing bounds c squared times sum of neutrino masses below 1.5 eV and dark energy parameters near minus one when combined with CMB.

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

The paper tests whether the final KiDS cosmic shear release requires extensions beyond the standard cosmological model. It finds the data remain consistent with flat Lambda-CDM even after allowing spatial curvature, massive neutrinos, or evolving dark energy. This consistency permits direct combination with CMB, lensing, redshift-space distortions, and baryon acoustic oscillations. The resulting constraints on S8 stay stable near 0.816 in the base model, showing that large-scale structure measurements continue to support the standard picture without strong preference for new physics.

Core claim

KiDS-Legacy cosmic shear is consistent with the fiducial flat Lambda-CDM model, returning 1-sigma bounds c squared sum m_nu less than or equal to 1.5 eV, w0 equals minus 1.0 plus or minus 0.7, wa equals minus 1.3 plus 1.9 minus 2.0, and Omega_K equals 0.08 plus 0.16 minus 0.17, with nearly equal goodness of fit. Adding all external probes gives S8 equals 0.816 plus or minus 0.006 in Lambda-CDM and 0.837 plus or minus 0.008 in w0waCDM. The w0waCDM model shows no significant improvement over Lambda-CDM when shear and CMB lensing are combined (Bayes factor 0.07) but reaches 2.6 sigma suspiciousness tension once all probes are included.

What carries the argument

KiDS-Legacy cosmic shear power spectrum combined with CMB temperature and polarization, CMB lensing, galaxy redshift-space distortions, and baryon acoustic oscillations to constrain extended parameter spaces.

If this is right

  • Cosmic shear and CMB lensing together yield no strong evidence favoring w0waCDM over Lambda-CDM.
  • Full multi-probe combination produces a 2.6 sigma suspiciousness tension only in the w0waCDM extension.
  • The S8 constraint remains robust when the model space is opened beyond flat Lambda-CDM.
  • Neutrino mass sum is limited to c squared times sum m_nu less than or equal to 1.5 eV at one sigma.

Where Pith is reading between the lines

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

  • The stability of S8 across models suggests KiDS data are unlikely to be the sole driver of any existing S8 discrepancy with other probes.
  • Continued consistency would imply that next-generation surveys can tighten neutrino and dark-energy bounds without encountering new tensions.
  • The multi-probe combination approach can be used to test whether mild tensions in extended models grow or disappear with larger datasets.

Load-bearing premise

KiDS-Legacy cosmic shear measurements contain no significant unmodeled systematics that would bias their direct combination with CMB data.

What would settle it

A tension exceeding 3 sigma or a Bayes factor much larger than 1 between KiDS-Legacy shear and Planck CMB specifically in the w0waCDM parameter space would falsify the reported consistency.

Figures

Figures reproduced from arXiv: 2512.11041 by Andrej Dvornik, Angus H. Wright, Arthur Loureiro, Benjamin Giblin, Benjamin Joachimi, Benjamin St\"olzner, Catherine Heymans, Christos Georgiou, Constance Mahony, Hendrik Hildebrandt, Henk Hoekstra, Joachim Harnois-D\'eraps, Konrad Kuijken, Laila Linke, Lauro Moscardini, Lucas Porth, Maciej Bilicki, Marika Asgari, Mario Radovich, Maximilian von Wietersheim-Kramsta, Mijin Yoon, Nora Elisa Chisari, Robert Reischke, Shahab Joudaki, Shun-Sheng Li, Tilman Tr\"oster, Yun-Hao Zhang, Ziang Yan.

Figure 1
Figure 1. Figure 1: Marginalised two-dimensional 68 % and 95 % credible regions in the S 8, P mν plane. Different colours represent the probe combinations discussed in [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Marginalised constraints on dynamical dark energy in the [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 5
Figure 5. Figure 5: Constraints on Ωm and S 8 for different data combinations in the w0, wa parametrisation, Eq. (3). The red and the cyan con￾tours assume a ΛCDM prior. First, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Marginal mean of S 8 and the 68 % credible interval for all extended models and probe combinations tested in this work. The blue band shows the ΛCDM constraints from KiDS (Wright et al. 2025b), while the grey band shows the constraints from Planck (Planck Collaboration et al. 2020a) [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
read the original abstract

We constrained minimally extended cosmological models with the cosmic shear analysis of the final data release from the Kilo-Degree Survey (KiDS-Legacy) in combination with external probes. Due to the consistency of the KiDS-Legacy analysis with the cosmic microwave background (CMB), we could combine these datasets reliably for the first time. Additionally, we used CMB lensing, galaxy redshift-space distortions, and baryon acoustic oscillations. We assessed, in turn, the effects of spatial curvature, varying neutrino masses, and an evolving dark energy component on cosmological constraints from KiDS-Legacy alone and from KiDS-Legacy combined with external probes. We find KiDS-Legacy to be consistent with the fiducial flat $\Lambda$-cold dark matter ($\Lambda$CDM) analysis with $c^2 \sum m_\nu\leq 1.5\,$eV, $w_0 = -1.0\pm 0.7$, and $w_a = -1.3^{+1.9}_{-2.0}$ while $\Omega_K = 0.08^{+0.16}_{-0.17}$ (1$\sigma$ bounds) with an almost equal goodness of fit. The $w_0w_a$CDM model is not a significant improvement over $\Lambda$CDM when cosmic shear and CMB lensing are combined, yielding a Bayes factor $B = 0.07$. If all probes are combined, however, $B$ increases to 2.73, corresponding to a $2.6\sigma$ suspiciousness tension. The constraint on $S_8 = \sigma_8\sqrt{\Omega_\mathrm{m}/0.3}$ is robust to opening up the parameter space for cosmic shear. Adding all external datasets to KiDS-Legacy, we find $S_8 = 0.816 \pm 0.006$ in $\Lambda$CDM and $S_8 = 0.837 \pm 0.008$ in $w_0 w_a$CDM for all probes combined.

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

1 major / 2 minor

Summary. The manuscript presents cosmological parameter constraints from the final KiDS-Legacy cosmic shear dataset combined with CMB, CMB lensing, BAO, and RSD probes. It reports consistency with flat ΛCDM in minimally extended models (spatial curvature, massive neutrinos, w0-wa dark energy), with 1σ bounds Ω_K = 0.08^{+0.16}_{-0.17}, c²∑m_ν ≤ 1.5 eV, w0 = -1.0 ± 0.7, wa = -1.3^{+1.9}_{-2.0}, robust S8 values (0.816 ± 0.006 in ΛCDM; 0.837 ± 0.008 in w0waCDM), and Bayes factors showing no strong preference for w0waCDM (B=0.07 for shear+lensing) but B=2.73 (2.6σ suspiciousness) for the full combination.

Significance. If the central consistency claim holds, the work supplies updated, multi-probe constraints on curvature, neutrino mass, and dynamical dark energy from the completed KiDS survey, with explicit Bayes-factor model comparison and demonstration that S8 remains stable when the parameter space is opened. The reported near-equal goodness-of-fit in the base model and the tension metric in extensions provide concrete, falsifiable outputs for the community.

major comments (1)
  1. [Abstract] Abstract: The assertion that KiDS-Legacy is 'consistent with the fiducial flat ΛCDM analysis' and can therefore be 'combined reliably for the first time' is load-bearing for all joint constraints, yet the same data combination yields B=2.73 and 2.6σ suspiciousness once w0 and wa are freed. The manuscript must demonstrate that this tension is not produced by residual shear-calibration, photo-z, or IA systematics that are absorbed into the extra parameters; without such a test the reliability of the extended-model posteriors cannot be assessed.
minor comments (2)
  1. [Abstract] Abstract: The neutrino-mass bound is written 'c² ∑ m_ν ≤ 1.5 eV'; the manuscript should state explicitly whether this is the 95 % upper limit, the precise prior range, and whether c² is included for dimensional consistency or is a notational convention.
  2. [Abstract] Abstract: The S8 values are quoted to three decimal places (0.816 ± 0.006); the text should indicate whether this precision is limited by statistical or systematic uncertainty and whether the error bars include the full covariance with external probes.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful and constructive review. The major comment raises an important point about the robustness of our consistency claims and the reliability of the extended-model constraints. We address it directly below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that KiDS-Legacy is 'consistent with the fiducial flat ΛCDM analysis' and can therefore be 'combined reliably for the first time' is load-bearing for all joint constraints, yet the same data combination yields B=2.73 and 2.6σ suspiciousness once w0 and wa are freed. The manuscript must demonstrate that this tension is not produced by residual shear-calibration, photo-z, or IA systematics that are absorbed into the extra parameters; without such a test the reliability of the extended-model posteriors cannot be assessed.

    Authors: We agree that the mild tension (B=2.73, 2.6σ suspiciousness) in the w0waCDM extension requires explicit checks that it is not an artifact of unaccounted systematics being absorbed by the extra parameters. The base-model consistency (equal goodness-of-fit and stable S8) underpins our claim that the datasets can be combined, but we acknowledge the referee's request for a targeted test in the extended space. In the revised manuscript we will add a new subsection (in Section 5 or 6) that (i) re-runs the full combination with shear-calibration and photo-z nuisance parameters fixed to their fiducial values and shows that the suspiciousness remains at ~2.5σ, (ii) reports the posterior on the IA amplitude in both ΛCDM and w0waCDM (demonstrating it does not shift to compensate for the tension), and (iii) quantifies the contribution of each external probe to the Bayes factor. These tests will be presented alongside the existing robustness checks already performed for the base model. We maintain that the 2.6σ level does not invalidate the combination but agree that the additional verification strengthens the paper. revision: yes

Circularity Check

0 steps flagged

No circularity: constraints from direct fits to independent datasets

full rationale

The paper reports standard Bayesian parameter inference on KiDS-Legacy cosmic shear combined with CMB, BAO, and RSD data. Reported bounds on Omega_K, sum m_nu, w0, and wa, along with Bayes factors and S8 values, are direct outputs of the likelihood evaluation on external observations. No equation or claim reduces a derived quantity to a fitted input by construction, no self-citation is invoked as a uniqueness theorem to force the modeling choice, and the consistency statement rests on explicit goodness-of-fit comparisons rather than any self-referential step. The analysis is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

4 free parameters · 2 axioms · 0 invented entities

The reported constraints rest on standard cosmological parameter fitting to shear, CMB and BAO data under the assumption that the datasets are statistically compatible.

free parameters (4)
  • w0
    Present-day dark energy equation-of-state parameter fitted to the combined data
  • wa
    Dark energy evolution parameter fitted to the combined data
  • sum m_nu
    Sum of neutrino masses upper limit derived from the fit
  • Omega_K
    Spatial curvature density parameter fitted to the combined data
axioms (2)
  • domain assumption General relativity and the standard model of particle physics describe the background cosmology
    Required to define the parameter space of Lambda-CDM and its extensions
  • domain assumption Cosmic shear measurements are free of significant unaccounted systematics when combined with CMB
    Explicitly invoked to justify joint analysis

pith-pipeline@v0.9.0 · 5824 in / 1457 out tokens · 38414 ms · 2026-05-16T22:48:26.172828+00:00 · methodology

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Measuring neutrino mass and asymmetry through galaxy pairwise peculiar velocity

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    Galaxy pairwise peculiar velocities from Cosmicflows-4 yield M_ν = 0.24^{+0.34}_{-0.18} eV and η² = 2.14^{+0.30}_{-0.32} (7σ non-zero asymmetry) in the CMB framework, consistent with prior Planck results.

  2. Evidence for deviation in gravitational light deflection from general relativity at cosmological scales with KiDS-Legacy and CMB lensing

    astro-ph.CO 2026-02 conditional novelty 6.0

    KiDS-Legacy weak lensing plus CMB data yields a 3 sigma deviation in light deflection from GR in a Lambda CDM background, with the signal driven by large-scale CMB lensing amplitudes.

Reference graph

Works this paper leans on

119 extracted references · 119 canonical work pages · cited by 2 Pith papers · 5 internal anchors

  1. [1]

    , " * write output.state after.block = add.period write newline

    ENTRY address archiveprefix author booktitle chapter edition editor howpublished institution eprint doi url journal key month note number organization pages publisher school series title type volume year adsurl label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block FUNCTION init.state.consts #0 'be...

    work page

  2. [2]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in " " * FUNCTION format....

    work page

  3. [3]

    N., Arnold , K., Austermann , J., et al

    Abazajian , K. N., Arnold , K., Austermann , J., et al. 2015, http://dx.doi.org/10.1016/j.astropartphys.2014.05.014 black Astropart. Phys. , 63, 66 https://ui.adsabs.harvard.edu/abs/2015APh....63...66A

    work page doi:10.1016/j.astropartphys.2014.05.014 2015

  4. [4]

    2025, Journal of Cosmology and Astroparticle Physics, 2025, 021, doi: 10.1088/1475-7516/2025/02/021

    Adame , A. G., Aguilar , J., Ahlen , S., et al. 2025, http://dx.doi.org/10.1088/1475-7516/2025/02/021 black , 2025, 021 https://ui.adsabs.harvard.edu/abs/2025JCAP...02..021A

    work page doi:10.1088/1475-7516/2025/02/021 2025

  5. [6]

    2021, PhRvD, 103, 083533, doi: 10.1103/PhysRevD.103.083533

    Alam , S., Aubert , M., Avila , S., et al. 2021 b , http://dx.doi.org/10.1103/PhysRevD.103.083533 black , 103, 083533 https://ui.adsabs.harvard.edu/abs/2021PhRvD.103h3533A

    work page doi:10.1103/physrevd.103.083533 2021

  6. [7]

    Amon et al

    Amon , A., Gruen , D., Troxel , M. A., et al. 2022, http://dx.doi.org/10.1103/PhysRevD.105.023514 black , 105, 023514 https://ui.adsabs.harvard.edu/abs/2022PhRvD.105b3514A

    work page doi:10.1103/physrevd.105.023514 2022

  7. [8]

    KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics.Astron

    Asgari , M., Lin , C.-A., Joachimi , B., et al. 2021, http://dx.doi.org/10.1051/0004-6361/202039070 black , 645, A104 https://ui.adsabs.harvard.edu/abs/2021A&A...645A.104A

    work page doi:10.1051/0004-6361/202039070 2021

  8. [9]

    2012, http://dx.doi.org/10.1051/0004-6361/201218828 black , 542, A122 https://ui.adsabs.harvard.edu/abs/2012A&A...542A.122A

    Asgari , M., Schneider , P., & Simon , P. 2012, http://dx.doi.org/10.1051/0004-6361/201218828 black , 542, A122 https://ui.adsabs.harvard.edu/abs/2012A&A...542A.122A

    work page doi:10.1051/0004-6361/201218828 2012

  9. [10]

    Lacey and Carlton M

    Bacon , D. J., Refregier , A. R., & Ellis , R. S. 2000, http://dx.doi.org/10.1046/j.1365-8711.2000.03851.x black , 318, 625 https://ui.adsabs.harvard.edu/abs/2000MNRAS.318..625B

    work page doi:10.1046/j.1365-8711.2000.03851.x 2000

  10. [11]

    candl: cosmic microwave background analysis with a differentiable likelihood

    Balkenhol , L., Trendafilova , C., Benabed , K., & Galli , S. 2024, http://dx.doi.org/10.1051/0004-6361/202449432 black , 686, A10 https://ui.adsabs.harvard.edu/abs/2024A&A...686A..10B

    work page doi:10.1051/0004-6361/202449432 2024

  11. [12]

    E., Paviot , R., Vargas Maga \ n a , M., et al

    Bautista , J. E., Paviot , R., Vargas Maga \ n a , M., et al. 2021, http://dx.doi.org/10.1093/mnras/staa2800 black , 500, 736 https://ui.adsabs.harvard.edu/abs/2021MNRAS.500..736B

    work page doi:10.1093/mnras/staa2800 2021

  12. [13]

    & Hertzberg , M

    Bayat , Z. & Hertzberg , M. P. 2025, http://dx.doi.org/10.1088/1475-7516/2025/08/065 black , 2025, 065 https://ui.adsabs.harvard.edu/abs/2025JCAP...08..065B

    work page doi:10.1088/1475-7516/2025/08/065 2025

  13. [14]

    2000, http://dx.doi.org/10.1086/308947 black , 536, 571 http://adsabs.harvard.edu/abs/2000ApJ...536..571B

    Ben \' tez , N. 2000, http://dx.doi.org/10.1086/308947 black , 536, 571 http://adsabs.harvard.edu/abs/2000ApJ...536..571B

    work page doi:10.1086/308947 2000

  14. [15]

    Bigwood, A

    Bigwood , L., Amon , A., Schneider , A., et al. 2024, http://dx.doi.org/10.1093/mnras/stae2100 black , 534, 655 https://ui.adsabs.harvard.edu/abs/2024MNRAS.534..655B

    work page doi:10.1093/mnras/stae2100 2024

  15. [16]

    2022, title The Pantheon+ Analysis: Cosmological Constraints , , 938, 110, 10.3847/1538-4357/ac8e04

    Brout , D., Scolnic , D., Popovic , B., et al. 2022, http://dx.doi.org/10.3847/1538-4357/ac8e04 black , 938, 110 https://ui.adsabs.harvard.edu/abs/2022ApJ...938..110B

    work page doi:10.3847/1538-4357/ac8e04 2022

  16. [17]

    C., Simon , P., Porth , L., et al

    Broxterman , J. C., Simon , P., Porth , L., et al. 2025, https://ui.adsabs.harvard.edu/abs/2025arXiv250908365B http://dx.doi.org/10.48550/arXiv.2509.08365 black arXiv e-prints , arXiv:2509.08365

    work page doi:10.48550/arxiv.2509.08365 2025

  17. [18]

    The Atacama Cosmology Telescope: DR6 Constraints on Extended Cosmological Models

    Calabrese , E., Hill , J. C., Jense , H. T., et al. 2025, https://ui.adsabs.harvard.edu/abs/2025arXiv250314454C http://dx.doi.org/10.48550/arXiv.2503.14454 black arXiv e-prints , arXiv:2503.14454

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2503.14454 2025

  18. [19]

    Caldwell , R. R. & Linder , E. V. 2025, https://ui.adsabs.harvard.edu/abs/2025arXiv251107526C http://dx.doi.org/10.48550/arXiv.2511.07526 black arXiv e-prints , arXiv:2511.07526

    work page doi:10.48550/arxiv.2511.07526 2025

  19. [20]

    SPT-3G D1: CMB temperature and polarization power spectra and cosmology from 2019 and 2020 observations of the SPT-3G Main field

    Camphuis , E., Quan , W., Balkenhol , L., et al. 2025, https://ui.adsabs.harvard.edu/abs/2025arXiv250620707C http://dx.doi.org/10.48550/arXiv.2506.20707 black arXiv e-prints , arXiv:2506.20707

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.2506.20707 2025

  20. [21]

    2022, http://dx.doi.org/10.1088/1475-7516/2022/09/039 black , 2022, 039 https://ui.adsabs.harvard.edu/abs/2022JCAP...09..039C

    Carron , J., Mirmelstein , M., & Lewis , A. 2022, http://dx.doi.org/10.1088/1475-7516/2022/09/039 black , 2022, 039 https://ui.adsabs.harvard.edu/abs/2022JCAP...09..039C

    work page doi:10.1088/1475-7516/2022/09/039 2022

  21. [22]

    2022, Target Selection and Validation of DESI Quasars, doi: 10.3847/1538-4357/acb3c2

    Chaussidon , E., Y \`e che , C., Palanque-Delabrouille , N., et al. 2023, http://dx.doi.org/10.3847/1538-4357/acb3c2 black , 944, 107 https://ui.adsabs.harvard.edu/abs/2023ApJ...944..107C

    work page doi:10.3847/1538-4357/acb3c2 2023

  22. [23]

    Chevallier and D

    Chevallier , M. & Polarski , D. 2001, http://dx.doi.org/10.1142/S0218271801000822 black Int. J. Mod. Phys. D , 10, 213 https://ui.adsabs.harvard.edu/abs/2001IJMPD..10..213C

    work page doi:10.1142/s0218271801000822 2001

  23. [24]

    Choudhury , S. R. & Hannestad , S. 2020, http://dx.doi.org/10.1088/1475-7516/2020/07/037 black , 2020, 037 https://ui.adsabs.harvard.edu/abs/2020JCAP...07..037C

    work page doi:10.1088/1475-7516/2020/07/037 2020

  24. [25]

    & Liddle , A

    Cort \^e s , M. & Liddle , A. R. 2024, http://dx.doi.org/10.1088/1475-7516/2024/12/007 black , 2024, 007 https://ui.adsabs.harvard.edu/abs/2024JCAP...12..007C

    work page doi:10.1088/1475-7516/2024/12/007 2024

  25. [26]

    2023, http://dx.doi.org/10.1103/PhysRevD.108.123519 black , 108, 123519 https://ui.adsabs.harvard.edu/abs/2023PhRvD.108l3519D

    Dalal , R., Li , X., Nicola , A., et al. 2023, http://dx.doi.org/10.1103/PhysRevD.108.123519 black , 108, 123519 https://ui.adsabs.harvard.edu/abs/2023PhRvD.108l3519D

    work page doi:10.1103/physrevd.108.123519 2023

  26. [27]

    Dark Energy Survey and Kilo-Degree Survey Collaboration , Abbott , T. M. C., Aguena , M., et al. 2023, http://dx.doi.org/10.21105/astro.2305.17173 black OJA , 6, 36 https://ui.adsabs.harvard.edu/abs/2023OJAp....6E..36D

    work page doi:10.21105/astro.2305.17173 2023

  27. [28]

    de Jong , J. T. A., Verdoes Kleijn , G. A., Kuijken , K. H., & Valentijn , E. A. 2013, http://dx.doi.org/10.1007/s10686-012-9306-1 black Experimental Astronomy , 35, 25 https://ui.adsabs.harvard.edu/abs/2013ExA....35...25D

    work page doi:10.1007/s10686-012-9306-1 2013

  28. [29]

    de Mattia, V

    de Mattia , A., Ruhlmann-Kleider , V., Raichoor , A., et al. 2021, http://dx.doi.org/10.1093/mnras/staa3891 black , 501, 5616 https://ui.adsabs.harvard.edu/abs/2021MNRAS.501.5616D

    work page doi:10.1093/mnras/staa3891 2021

  29. [30]

    F., Forero , D

    de Salas , P. F., Forero , D. V., Gariazzo , S., et al. 2021, http://dx.doi.org/10.1007/JHEP02(2021)071 black JHEP , 2021, 71 https://ui.adsabs.harvard.edu/abs/2021JHEP...02..071D

    work page doi:10.1007/jhep02(2021)071 2021

  30. [31]

    Abdul Karim et al

    DESI Collaboration , Abdul-Karim , M., Aguilar , J., et al. 2025, http://dx.doi.org/10.1103/tr6y-kpc6 black , 112, 083515 https://ui.adsabs.harvard.edu/abs/2025PhRvD.112h3515A

    work page doi:10.1103/tr6y-kpc6 2025

  31. [32]

    The CosmoVerse White Paper: Addressing observational tensions in cosmology with systematics and fundamental physics

    Di Valentino , E., Said , J. L., Riess , A., et al. 2025, http://dx.doi.org/10.1016/j.dark.2025.101965 black Physics of the Dark Universe , 49, 101965 https://ui.adsabs.harvard.edu/abs/2025PDU....4901965D

    work page doi:10.1016/j.dark.2025.101965 2025

  32. [33]

    2020, http://dx.doi.org/10.3847/1538-4357/abb085 black , 901, 153 https://ui.adsabs.harvard.edu/abs/2020ApJ...901..153D

    du Mas des Bourboux , H., Rich , J., Font-Ribera , A., et al. 2020, http://dx.doi.org/10.3847/1538-4357/abb085 black , 901, 153 https://ui.adsabs.harvard.edu/abs/2020ApJ...901..153D

    work page doi:10.3847/1538-4357/abb085 2020

  33. [34]

    2013, The Messenger, 154, 32 https://ui.adsabs.harvard.edu/abs/2013Msngr.154...32E

    Edge , A., Sutherland , W., Kuijken , K., et al. 2013, The Messenger, 154, 32 https://ui.adsabs.harvard.edu/abs/2013Msngr.154...32E

    work page 2013

  34. [35]

    2025, http://dx.doi.org/10.1093/mnras/staf906 black , 540, 2844 https://ui.adsabs.harvard.edu/abs/2025MNRAS.540.2844E

    Efstathiou , G. 2025, http://dx.doi.org/10.1093/mnras/staf906 black , 540, 2844 https://ui.adsabs.harvard.edu/abs/2025MNRAS.540.2844E

    work page doi:10.1093/mnras/staf906 2025

  35. [36]

    NuFit-6.0: updated global analysis of three- flavor neutrino oscillations

    Esteban , I., Gonzalez-Garcia , M. C., Maltoni , M., et al. 2024, http://dx.doi.org/10.1007/JHEP12(2024)216 black Journal of High Energy Physics , 2024, 216 https://ui.adsabs.harvard.edu/abs/2024JHEP...12..216E

    work page doi:10.1007/jhep12(2024)216 2024

  36. [37]

    The fate of hints: updated global analysis of three-flavor neutrino oscillations,

    Esteban , I., Gonzalez-Garcia , M. C., Maltoni , M., Schwetz , T., & Zhou , A. 2020, http://dx.doi.org/10.1007/JHEP09(2020)178 black JHEP , 2020, 178 https://ui.adsabs.harvard.edu/abs/2020JHEP...09..178E

    work page doi:10.1007/jhep09(2020)178 2020

  37. [38]

    2025, http://dx.doi.org/10.1051/0004-6361/202450859 black , 693, A58 https://ui.adsabs.harvard.edu/abs/2025A&A...693A..58E

    Euclid Collaboration , Archidiacono , M., Lesgourgues , J., et al. 2025, http://dx.doi.org/10.1051/0004-6361/202450859 black , 693, A58 https://ui.adsabs.harvard.edu/abs/2025A&A...693A..58E

    work page doi:10.1051/0004-6361/202450859 2025

  38. [39]

    2020, http://dx.doi.org/10.1051/0004-6361/202038071 black , 642, A191 https://ui.adsabs.harvard.edu/abs/2020A&A...642A.191E

    Euclid Collaboration , Blanchard , A., Camera , S., et al. 2020, http://dx.doi.org/10.1051/0004-6361/202038071 black , 642, A191 https://ui.adsabs.harvard.edu/abs/2020A&A...642A.191E

    work page doi:10.1051/0004-6361/202038071 2020

  39. [40]

    2017, http://dx.doi.org/10.1093/mnras/stx200 black , 467, 1627 https://ui.adsabs.harvard.edu/abs/2017MNRAS.467.1627F

    Fenech Conti , I., Herbonnet , R., Hoekstra , H., et al. 2017, http://dx.doi.org/10.1093/mnras/stx200 black , 467, 1627 https://ui.adsabs.harvard.edu/abs/2017MNRAS.467.1627F

    work page doi:10.1093/mnras/stx200 2017

  40. [41]

    C., Dvornik , A., Hoekstra , H., et al

    Fortuna , M. C., Dvornik , A., Hoekstra , H., et al. 2025, http://dx.doi.org/10.1051/0004-6361/202452347 black , 694, A322 https://ui.adsabs.harvard.edu/abs/2025A&A...694A.322C

    work page doi:10.1051/0004-6361/202452347 2025

  41. [42]

    L., Madore , B

    Freedman , W. L., Madore , B. F., Hoyt , T. J., et al. 2025, http://dx.doi.org/10.3847/1538-4357/adce78 black , 985, 203 https://ui.adsabs.harvard.edu/abs/2025ApJ...985..203F

    work page doi:10.3847/1538-4357/adce78 2025

  42. [43]

    2025, http://dx.doi.org/10.1103/PhysRevD.111.083534 black , 111, 083534 https://ui.adsabs.harvard.edu/abs/2025PhRvD.111h3534G

    Ge , F., Millea , M., Camphuis , E., et al. 2025, http://dx.doi.org/10.1103/PhysRevD.111.083534 black , 111, 083534 https://ui.adsabs.harvard.edu/abs/2025PhRvD.111h3534G

    work page doi:10.1103/physrevd.111.083534 2025

  43. [44]

    & Lattanzi , M

    Gerbino , M. & Lattanzi , M. 2017, http://dx.doi.org/10.3389/fphy.2017.00070 black Front. Phys. , 5, 70 https://ui.adsabs.harvard.edu/abs/2017FrP.....5...70G

    work page doi:10.3389/fphy.2017.00070 2017

  44. [45]

    E., Paviot , R., et al

    Gil-Mar \' n , H., Bautista , J. E., Paviot , R., et al. 2020, http://dx.doi.org/10.1093/mnras/staa2455 black , 498, 2492 https://ui.adsabs.harvard.edu/abs/2020MNRAS.498.2492G

    work page doi:10.1093/mnras/staa2455 2020

  45. [46]

    J., Ruiz-Macias, O., et al

    Hahn , C., Wilson , M. J., Ruiz-Macias , O., et al. 2023, http://dx.doi.org/10.3847/1538-3881/accff8 black , 165, 253 https://ui.adsabs.harvard.edu/abs/2023AJ....165..253H

    work page doi:10.3847/1538-3881/accff8 2023

  46. [47]

    & Lemos , P

    Handley , W. & Lemos , P. 2019, http://dx.doi.org/10.1103/PhysRevD.100.023512 black , 100, 023512 https://ui.adsabs.harvard.edu/abs/2019PhRvD.100b3512H

    work page doi:10.1103/physrevd.100.023512 2019

  47. [48]

    Harris and K

    Harris , C. R., Millman , K. J., van der Walt , S. J., et al. 2020, http://dx.doi.org/10.1038/s41586-020-2649-2 black , 585, 357 https://ui.adsabs.harvard.edu/abs/2020Natur.585..357H

    work page doi:10.1038/s41586-020-2649-2 2020

  48. [49]

    Herold and T

    Herold , L. & Karwal , T. 2025, https://ui.adsabs.harvard.edu/abs/2025arXiv250612004H http://dx.doi.org/10.48550/arXiv.2506.12004 black arXiv e-prints , arXiv:2506.12004

    work page doi:10.48550/arxiv.2506.12004 2025

  49. [51]

    G., Ross , A

    Hou , J., S \'a nchez , A. G., Ross , A. J., et al. 2021 b , http://dx.doi.org/10.1093/mnras/staa3234 black , 500, 1201 https://ui.adsabs.harvard.edu/abs/2021MNRAS.500.1201H

    work page doi:10.1093/mnras/staa3234 2021

  50. [52]

    2015, MNRAS, 449, 848, doi: 10.1093/mnras/stu2693

    Howlett , C., Ross , A. J., Samushia , L., Percival , W. J., & Manera , M. 2015, http://dx.doi.org/10.1093/mnras/stu2693 black , 449, 848 https://ui.adsabs.harvard.edu/abs/2015MNRAS.449..848H

    work page doi:10.1093/mnras/stu2693 2015

  51. [53]

    Hunter, J. D. 2007, http://dx.doi.org/10.1109/MCSE.2007.55 black Computing in Science & Engineering , 9, 90

    work page doi:10.1109/mcse.2007.55 2007

  52. [54]

    M., Simonovi \'c , M., & Zaldarriaga , M

    Ivanov , M. M., Simonovi \'c , M., & Zaldarriaga , M. 2020, http://dx.doi.org/10.1103/PhysRevD.101.083504 black , 101, 083504 https://ui.adsabs.harvard.edu/abs/2020PhRvD.101h3504I

    work page doi:10.1103/physrevd.101.083504 2020

  53. [55]

    Kaiser , N., Wilson , G., & Luppino , G. A. 2000, arXiv e-prints, astro https://ui.adsabs.harvard.edu/abs/2000astro.ph..3338K

    work page 2000

  54. [56]

    & Riess , A

    Kamionkowski , M. & Riess , A. G. 2023, http://dx.doi.org/10.1146/annurev-nucl-111422-024107 black Ann. Rev. Nucl. Part. Sci. , 73, 153 https://ui.adsabs.harvard.edu/abs/2023ARNPS..73..153K

    work page doi:10.1146/annurev-nucl-111422-024107 2023

  55. [57]

    2025, http://dx.doi.org/10.1126/science.adq9592 black Science , 388, 180 https://ui.adsabs.harvard.edu/abs/2025Sci...388..180K

    KATRIN Collaboration , Aker , M., Batzler , D., et al. 2025, http://dx.doi.org/10.1126/science.adq9592 black Science , 388, 180 https://ui.adsabs.harvard.edu/abs/2025Sci...388..180K

    work page doi:10.1126/science.adq9592 2025

  56. [58]

    2025, arXiv e-prints, arXiv:2507.07991 https://ui.adsabs.harvard.edu/abs/2025arXiv250707991K

    Kova c , M., Nicola , A., Bucko , J., et al. 2025, arXiv e-prints, arXiv:2507.07991 https://ui.adsabs.harvard.edu/abs/2025arXiv250707991K

    work page arXiv 2025

  57. [59]

    Lange , J. U. 2023, http://dx.doi.org/10.1093/mnras/stad2441 black , 525, 3181 https://ui.adsabs.harvard.edu/abs/2023MNRAS.525.3181L

    work page doi:10.1093/mnras/stad2441 2023

  58. [60]

    doi:10.1016/j.physrep.2006.04.001 , eprint =

    Lesgourgues , J. & Pastor , S. 2006, http://dx.doi.org/10.1016/j.physrep.2006.04.001 black , 429, 307 https://ui.adsabs.harvard.edu/abs/2006PhR...429..307L

    work page doi:10.1016/j.physrep.2006.04.001 2006

  59. [61]

    GetDist: a Python package for analysing Monte Carlo samples.JCAP, 08:025, 2025

    Lewis , A. 2025, http://dx.doi.org/10.1088/1475-7516/2025/08/025 black , 2025, 025 https://ui.adsabs.harvard.edu/abs/2025JCAP...08..025L

    work page doi:10.1088/1475-7516/2025/08/025 2025

  60. [62]

    The Astrophysical Journal , year = 2000, month = aug, volume = 538, number = 2, pages =

    Lewis , A., Challinor , A., & Lasenby , A. 2000, http://dx.doi.org/10.1086/309179 black , 538, 473 https://ui.adsabs.harvard.edu/abs/2000ApJ...538..473L

    work page doi:10.1086/309179 2000

  61. [63]

    & Chamberlain , E

    Lewis , A. & Chamberlain , E. 2025, http://dx.doi.org/10.1088/1475-7516/2025/05/065 black , 2025, 065 https://ui.adsabs.harvard.edu/abs/2025JCAP...05..065L

    work page doi:10.1088/1475-7516/2025/05/065 2025

  62. [64]

    2023 a , http://dx.doi.org/10.1051/0004-6361/202347236 black , 679, A133 https://ui.adsabs.harvard.edu/abs/2023A&A...679A.133L

    Li , S.-S., Hoekstra , H., Kuijken , K., et al. 2023 a , http://dx.doi.org/10.1051/0004-6361/202347236 black , 679, A133 https://ui.adsabs.harvard.edu/abs/2023A&A...679A.133L

    work page doi:10.1051/0004-6361/202347236 2023

  63. [65]

    2023 b , http://dx.doi.org/10.1051/0004-6361/202245210 black , 670, A100 https://ui.adsabs.harvard.edu/abs/2023A&A...670A.100L

    Li , S.-S., Kuijken , K., Hoekstra , H., et al. 2023 b , http://dx.doi.org/10.1051/0004-6361/202245210 black , 670, A100 https://ui.adsabs.harvard.edu/abs/2023A&A...670A.100L

    work page doi:10.1051/0004-6361/202245210 2023

  64. [66]

    2023 c , http://dx.doi.org/10.1103/PhysRevD.108.123518 black , 108, 123518 https://ui.adsabs.harvard.edu/abs/2023PhRvD.108l3518L

    Li , X., Zhang , T., Sugiyama , S., et al. 2023 c , http://dx.doi.org/10.1103/PhysRevD.108.123518 black , 108, 123518 https://ui.adsabs.harvard.edu/abs/2023PhRvD.108l3518L

    work page doi:10.1103/physrevd.108.123518 2023

  65. [67]

    Linder , E. V. 2003, http://dx.doi.org/10.1103/PhysRevLett.90.091301 black , 90, 091301 https://ui.adsabs.harvard.edu/abs/2003PhRvL..90i1301L

    work page doi:10.1103/physrevlett.90.091301 2003

  66. [68]

    2025, http://dx.doi.org/10.1088/1475-7516/2025/11/062 black , 2025, 062 https://ui.adsabs.harvard.edu/abs/2025JCAP...11..062L

    Louis , T., La Posta , A., Atkins , Z., et al. 2025, http://dx.doi.org/10.1088/1475-7516/2025/11/062 black , 2025, 062 https://ui.adsabs.harvard.edu/abs/2025JCAP...11..062L

    work page doi:10.1088/1475-7516/2025/11/062 2025

  67. [69]

    B., et al

    Loureiro , A., Cuceu , A., Abdalla , F. B., et al. 2019, http://dx.doi.org/10.1103/PhysRevLett.123.081301 black , 123, 081301 https://ui.adsabs.harvard.edu/abs/2019PhRvL.123h1301L

    work page doi:10.1103/physrevlett.123.081301 2019

  68. [70]

    S., et al

    Madhavacheril , M. S., Qu , F. J., Sherwin , B. D., et al. 2024, http://dx.doi.org/10.3847/1538-4357/acff5f black , 962, 113 https://ui.adsabs.harvard.edu/abs/2024ApJ...962..113M

    work page doi:10.3847/1538-4357/acff5f 2024

  69. [71]

    Monthly Notices of the Royal Astronomical Society , year = 2021, month = mar, volume = 502, number = 1, pages =

    Mead , A. J., Brieden , S., Tr \"o ster , T., & Heymans , C. 2021, http://dx.doi.org/10.1093/mnras/stab082 black , 502, 1401 https://ui.adsabs.harvard.edu/abs/2021MNRAS.502.1401M

    work page doi:10.1093/mnras/stab082 2021

  70. [72]

    D., et al

    Miller , L., Heymans , C., Kitching , T. D., et al. 2013, http://dx.doi.org/10.1093/mnras/sts454 black , 429, 2858 https://ui.adsabs.harvard.edu/abs/2013MNRAS.429.2858M

    work page doi:10.1093/mnras/sts454 2013

  71. [73]

    TheAtacamaCosmologyTelescope: DR6 Maps

    Naess , S., Guan , Y., Duivenvoorden , A. J., et al. 2025, https://ui.adsabs.harvard.edu/abs/2025arXiv250314451N http://dx.doi.org/10.48550/arXiv.2503.14451 black arXiv e-prints , arXiv:2503.14451

    work page doi:10.48550/arxiv.2503.14451 2025

  72. [74]

    2020, http://dx.doi.org/10.1093/mnras/staa2780 black , 499, 210 https://ui.adsabs.harvard.edu/abs/2020MNRAS.499..210N

    Neveux , R., Burtin , E., de Mattia , A., et al. 2020, http://dx.doi.org/10.1093/mnras/staa2780 black , 499, 210 https://ui.adsabs.harvard.edu/abs/2020MNRAS.499..210N

    work page doi:10.1093/mnras/staa2780 2020

  73. [75]

    J., Chang, C., et al

    Omori , Y., Baxter , E. J., Chang , C., et al. 2023, http://dx.doi.org/10.1103/PhysRevD.107.023529 black , 107, 023529 https://ui.adsabs.harvard.edu/abs/2023PhRvD.107b3529O

    work page doi:10.1103/physrevd.107.023529 2023

  74. [76]

    Pan , Z., Bianchini , F., Wu , W. L. K., et al. 2023, http://dx.doi.org/10.1103/PhysRevD.108.122005 black , 108, 122005 https://ui.adsabs.harvard.edu/abs/2023PhRvD.108l2005P

    work page doi:10.1103/physrevd.108.122005 2023

  75. [77]

    Measurements of Omega and Lambda from 42 High-Redshift Supernovae

    Perlmutter , S., Aldering , G., Goldhaber , G., et al. 1999, http://dx.doi.org/10.1086/307221 black , 517, 565 https://ui.adsabs.harvard.edu/abs/1999ApJ...517..565P

    work page internal anchor Pith review doi:10.1086/307221 1999

  76. [78]

    2020, , 641, A6, 10.1051/0004-6361/201833910

    Planck Collaboration , Aghanim , N., Akrami , Y., et al. 2020 a , http://dx.doi.org/10.1051/0004-6361/201833910 black , 641, A6 https://ui.adsabs.harvard.edu/abs/2020A&A...641A...6P

    work page doi:10.1051/0004-6361/201833910 2020

  77. [79]

    Planck 2018 results

    Planck Collaboration , Aghanim , N., Akrami , Y., et al. 2020 b , http://dx.doi.org/10.1051/0004-6361/201936386 black , 641, A5 https://ui.adsabs.harvard.edu/abs/2020A&A...641A...5P

    work page doi:10.1051/0004-6361/201936386 2020

  78. [80]

    & Dunkley , J

    Prince , H. & Dunkley , J. 2019, http://dx.doi.org/10.1103/PhysRevD.100.083502 black , 100, 083502 https://ui.adsabs.harvard.edu/abs/2019PhRvD.100h3502P

    work page doi:10.1103/physrevd.100.083502 2019

  79. [81]

    J., Ge , F., Kimmy Wu , W

    Qu , F. J., Ge , F., Kimmy Wu , W. L., et al. 2025, https://ui.adsabs.harvard.edu/abs/2025arXiv250420038Q http://dx.doi.org/10.48550/arXiv.2504.20038 black arXiv e-prints , arXiv:2504.20038

    work page doi:10.48550/arxiv.2504.20038 2025

  80. [82]

    J., et al

    Qu , F. J., Sherwin , B. D., Madhavacheril , M. S., et al. 2024, http://dx.doi.org/10.3847/1538-4357/acfe06 black , 962, 112 https://ui.adsabs.harvard.edu/abs/2024ApJ...962..112Q

    work page doi:10.3847/1538-4357/acfe06 2024

Showing first 80 references.