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REVIEW 3 major objections 6 minor 150 references

Splitting today's matter density into geometry, growth, and early-universe pieces finds them compatible, yet their geometry–early difference sits 2σ from zero.

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2026-07-31 11:12 UTC pith:S66X3OGC

load-bearing objection Solid three-way Ω_m split that cleanly extends the DES/KiDS geometry–growth tests; the 2σ Δgeo,early flag is real under their partition but rests on untested assignment choices and forced CMB coupling. the 3 major comments →

arxiv 2607.28326 v1 pith:S66X3OGC submitted 2026-07-30 astro-ph.CO

Growth, geometry, and early-universe split of the matter density parameter Ω_(rm m)

Felicitas Keil , Isaac Tutusaus , Alain Blanchard This is my paper
classification astro-ph.CO PACS 98.80.Es98.80.-k95.36.+x
keywords matter density parametergeometry-growth splitearly universeΩm tensioncosmological consistency test3x2ptBAOCMB
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Cosmology's standard model is being stress-tested by asking whether the same present-day matter density is recovered when the physics that shape each observable are assigned to three separate regimes: background expansion and distances (geometry), structure formation (growth), and physics before recombination (early universe). Earlier splits stopped at geometry versus growth; this work adds the early-universe piece and applies the split to galaxy clustering and weak lensing, the cosmic microwave background, baryon acoustic oscillations, supernovae, and redshift-space distortions. The three matter-density values come out mutually consistent within roughly 1σ, with geometry and the early universe tightly correlated and growth more loosely constrained. Because that correlation shrinks the uncertainty on their difference to about 0.002, the difference itself lies 2σ from zero. A sympathetic reader cares because any genuine mismatch among regimes would be a clean internal inconsistency of the standard model, independent of the usual Hubble or S8 tensions.

Core claim

When Ωm is allowed three independent values—one for geometry, one for growth, and one for early-universe physics—and the same multi-probe data combination is analysed, the three posteriors remain compatible within ~1σ (Ωm^geo = 0.3064 ± 0.0051, Ωm^growth = 0.2855 ± 0.0221, Ωm^early = 0.3015 ± 0.0038), yet the tightly constrained difference ΔΩm^{geo,early} is 2σ away from zero.

What carries the argument

The three-regime phenomenological split of Ωm: every ingredient of each likelihood (linear power spectrum from the Boltzmann solver, growth-factor ODE and non-linear boost, window-function prefactors, sound-horizon integral or fit, luminosity and angular-diameter distances, multipole rescaling of the CMB spectra) is assigned to exactly one of geometry, growth, or early universe, producing three free matter densities that are sampled jointly.

Load-bearing premise

The assignment of every formula piece to exactly one regime is treated as a clean null test, even though several choices (which Hubble factors belong to geometry, whether the lensing prefactor is purely geometric, how much CMB growth information is simply cut rather than modelled) are judgment calls that could move the reported offset.

What would settle it

Re-run the identical data combination after moving the contested assignments (H′/H factors, weak-lensing prefactor, restored CMB lensing and high-ℓ scales modelled in the growth regime) and check whether ΔΩm^{geo,early} remains inconsistent with zero at ~2σ.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Geometry and early-universe matter densities stay strongly correlated once the full probe set is combined, so their difference is far better measured than either absolute value.
  • Growth remains the weakest of the three constraints and is only weakly correlated with the other two regimes.
  • The split model is mildly preferred by AIC over the single-Ωm analysis on the same data.
  • Adding genuine growth probes (cluster counts, CMB lensing) is the direct next step the paper identifies for tightening the growth posterior.

Where Pith is reading between the lines

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

  • The 2σ geometry–early offset may be an early, high-precision diagnostic of the same late-time expansion mismatch that appears as dynamical dark energy or an evolving Ωm in other analyses.
  • Because the sound-horizon fit and the multipole rescaling both tie early and geometric densities together, any future change in the early-physics modelling will shift the geometry posterior even if late-time data are held fixed.
  • If the offset survives more complete growth modelling, it supplies a concrete target for modified-gravity or early-dark-energy extensions that alter distances and the sound horizon differently.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The manuscript introduces a three-way phenomenological split of the present-day matter density parameter into geometry, growth, and early-universe regimes, extending prior geometry–growth splits. Using DES Y3 3×2pt, scale-cut Planck TT/TE/EE (no lensing), DESI DR2 BAO, Pantheon+ without SH0ES, and a compiled RSD set, the authors implement probe-specific assignments (power-spectrum rescaling Eqs. 4–8, CMB multipole rescaling Eq. 25, rd fitting formula Eq. 28, RSD fσ8 Eq. 31, WL window App. B) and sample the joint likelihood with Nautilus. They report Ω_m^geo = 0.3064±0.0051, Ω_m^growth = 0.2855±0.0221, Ω_m^early = 0.3015±0.0038 (mutually compatible within ~1σ), a strong geometry–early correlation, weak growth correlations, ΔAIC≈12.3 mildly favouring the split model, and ΔΩ_m^{geo,early} ≡ Ω_m^geo − Ω_m^early offset from zero at 2σ (σ_Δ≈0.002).

Significance. If the three-regime split is a faithful null test of ΛCDM, the work is a useful consistency diagnostic that cleanly separates early-universe physics from late-time geometry and growth, and that can be applied to forthcoming Stage-IV data. The explicit probe-by-probe modelling, the joint nested-sampling comparison to a non-split baseline, and the multi-survey combination are genuine strengths. The reported 2σ offset in ΔΩ_m^{geo,early} would be of interest for the proposed Ω_m tension and for dynamical-dark-energy interpretations, but only if it is shown to be robust against the phenomenological partition choices that set the geometry–early correlation.

major comments (3)
  1. [§5, Fig. 12; Eqs. 3, 25, 28; §3.2; App. B] The central 2σ claim on ΔΩ_m^{geo,early} (Abstract; §5; Fig. 12) rests on a strong geometry–early correlation whose size is largely fixed by modelling choices that are not stress-tested: CMB multipoles are computed with Ω_early then rigidly rescaled by d_A^geo/d_A^early (Eq. 25) with growth excised via scale cuts and no lensing (§3.2); r_d uses a ΛCDM fitting formula locked to Ω_early (Eq. 28) rather than a consistent EBS sound horizon; H′/H in the growth ODE is forced geometric even when Ω_m in that ODE is growth (Eq. 3, §2.2.1); and the WL window prefactor is labelled geometric via background ρ̄ (App. B). Under a true single-Ω_m ΛCDM universe, a slight mis-attribution can imprint a mean offset on Δ at the reported 0.002 level. The manuscript should either (i) rerun the joint chain under at least one alternate, physically motivated assignment set and show that the 2σ flag is stable, or
  2. [§3.2, §4, §5, Fig. 10–12] Growth is deliberately under-powered: CMB lensing and high-ℓ/ISW scales are removed rather than modelled in the growth regime (§3.2), and the growth posterior is prior-limited by EuclidEmulator2 when Planck is used alone (§4, §5). The statement that “all regimes are compatible” and that growth is uncorrelated with the others is therefore partly by construction. Either include a growth-sensitive CMB channel (lensing or a controlled high-ℓ subset) with an explicit growth assignment, or qualify the growth conclusions as limited by the current data cuts and state that the null test is primarily geometry vs early.
  3. [§5, Eq. 32] The AIC comparison (ΔAIC≈12.3, §5) is reported as slightly favouring the split model, but the split adds two free parameters whose posterior volume and prior boundaries (especially Ω_growth_m) are not fully characterised, and the non-split vs split χ² difference is not tabulated. Please report Δχ², effective parameter counts, and a Bayes factor or nested-model evidence ratio so that the model-preference statement can be assessed independently of AIC.
minor comments (6)
  1. [Figs. 1–7, A.1–A.2] Figs. 1–7 and A.1–A.2 vary one regime at a time around a fixed Planck-like cosmology; it would help the reader if the caption stated the fixed values of the other two Ω_m parameters and of H0, As, ns explicitly.
  2. [Abstract] The abstract states that ΔΩ_m^{geo,early} is 2σ from 0 while the absolute values are compatible; add the numerical value and uncertainty of Δ (≈0.0049±0.002) in the abstract for clarity.
  3. [§2.2.3, Eq. 28] Eq. (28) cites Brieden et al. (2023); briefly note the accuracy of this approximation over the prior range of Ω_early_m h² used in the chains, or show a comparison to CAMB r_d at the posterior edges.
  4. [§3.1, App. D] Appendix D shows MagLim vs redMaGiC agreement but is only mentioned briefly in §3.1; a one-sentence quantitative statement (e.g. shift in Ω_geo_m and Ω_early_m) in the main text would help.
  5. [§5] Typographical/consistency: “Plancklikelihood” and similar concatenations appear in several places (§5); space as “Planck likelihood”. Also standardise “non-split” vs “nonsplit”.
  6. [§3.5] The RSD compilation (Blanchard et al. 2024) overlaps in tracer/redshift with DESI; the claim that covariance is negligible (§3.5) should cite a quantitative bound or a leave-one-out test.

Circularity Check

0 steps flagged

No significant circularity: phenomenological three-regime null test fitted to external survey likelihoods; results are not forced by construction.

full rationale

The paper’s central claim is a consistency (null) test: under ΛCDM the three split matter densities should coincide when each probe’s ingredients are assigned to geometry, growth, or early-universe regimes. The data are external (DES Y3 3×2pt, scale-cut Planck, DESI DR2 BAO, Pantheon+ without SH0ES, compiled RSD). The split likelihoods (rescaled P_lin via G^growth/G^early, multipole axis rescaling by d_A^geo/d_A^early, r_d from Ω_early, WL window prefactor as geometric, etc.) enlarge the parameter space and induce a geo–early correlation that tightens σ(ΔΩ_m^{geo,early}); they do not algebraically force the posterior mean of Δ away from zero. No quantity is defined from the quantity it is said to predict; no parameter is fitted to a subset and then reported as an independent prediction of a near-identical observable; and no load-bearing uniqueness or ansatz is imported solely via overlapping-author citation. Modeling judgment calls (H′/H forced geometric, CMB growth excised rather than modeled, r_d ΛCDM fit formula) affect robustness/correctness of the null test, not circularity of the derivation. Self-contained against external benchmarks; score 0.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 1 invented entities

The central claim rests on standard flat-ΛCDM background and perturbation equations, public survey likelihoods, and a set of phenomenological partition rules that assign each formula factor to geometry, growth, or early physics. Two extra free densities are added relative to vanilla ΛCDM; no new physical fields are postulated. Load-bearing modeling axioms are the scale-independent growth ODE, the regime labels for window functions and H′/H, the rd fitting formula, and the deliberate removal of CMB growth channels.

free parameters (4)
  • Ω_m^geo = 0.3064 ± 0.0051
    Present-day matter density used in distances, WL/GC window geometric factors, and geometric pieces of the growth ODE; fitted in the joint likelihood.
  • Ω_m^growth = 0.2855 ± 0.0221
    Matter density entering the growth factor ODE, non-linear boost, IA amplitude, and fσ8; fitted jointly with large uncertainty.
  • Ω_m^early = 0.3015 ± 0.0038
    Matter density passed to the Einstein-Boltzmann solver and to the rd approximation; fitted jointly.
  • Standard ΛCDM + nuisance set (H0, ω_b, n_s, A_s, σ8/S8, DES biases/IA/photo-z/m, Planck foregrounds, SN M0)
    All non-split cosmological and survey nuisance parameters varied as in the baseline DES Y3 / Planck analyses; shifts in A_s and related parameters are reported relative to the non-split run.
axioms (6)
  • domain assumption Scale-independent linear growth factor obeying the second-order ODE in Eq. 3, with H′/H evaluated in the geometry regime even when Ω_m in the source term is Ω_m^growth.
    Stated in §2.2.1; massive neutrinos and some modified-gravity models violate scale independence, which the authors explicitly neglect for the null test.
  • ad hoc to paper Weak-lensing window prefactor proportional to Ω_m is geometric because it descends from the background density in the Poisson equation (App. B).
    Alternative literature choices exist; the paper argues via Bartelmann & Schneider derivation but the geometry vs growth label remains a modeling choice.
  • ad hoc to paper CMB information used here is only primordial + distance-to-last-scattering; lensing, ISW, and ℓ>396 (and low-ℓ TT) are removed so growth does not enter (§3.2).
    Excision rather than explicit growth modeling; authors defer CMB lensing to future work, which weakens the growth-regime constraint by construction.
  • domain assumption Sound horizon rd is given by the Brieden et al. (2023) ΛCDM fitting formula evaluated at Ω_m^early (Eq. 28), not by a free early-physics model.
    Ties the early regime to standard recombination physics; any true early-universe new physics would be only partially captured.
  • domain assumption Flat ΛCDM background distances and standard Limber/non-Limber projections as in DES Y3 CosmoSIS pipeline.
    Baseline cosmology assumed throughout; the split is a consistency test inside that framework, not a free-curvature or w(z) analysis.
  • domain assumption RSD compilation measurements are independent of each other and of DESI BAO covariance (§3.5).
    Authors argue negligible covariance from differing tracers/observables; if wrong, joint growth constraints are over-tightened.
invented entities (1)
  • Three-regime phenomenological Ω_m split (Ω_m^geo, Ω_m^growth, Ω_m^early) no independent evidence
    purpose: Allow separate inference of matter density from expansion/distances, structure growth, and pre-recombination physics as a ΛCDM consistency null test.
    Not a new particle or force; a parameter bookkeeping device. Independent meaning exists only insofar as different observables truly isolate those regimes—the paper’s own figures show residual cross-talk.

pith-pipeline@v1.2.0-daily-grok45 · 25141 in / 4164 out tokens · 79391 ms · 2026-07-31T11:12:37.564754+00:00 · methodology

0 comments
read the original abstract

While the $\Lambda$ cold dark matter ($\Lambda$CDM) model can successfully reproduce the measurements of many cosmological probes, some discrepancies have recently emerged. Therefore, it is necessary to test the standard cosmological model for consistency. An important stress test is to separate the influence of different cosmological regimes on the parameter inference. We treat three regimes separately here: geometry, growth, and the early universe. The geometrical regime concerns the expansion and curvature history, while the growth regime governs structure formation and the early-universe regime affects physics prior to recombination. Previous analyses have performed the split between geometry and growth, whereas we also consider the early universe influence separately. We perform this split for the present day matter density parameter $\Omega_{\rm m}$ using multiple cosmological observables. The used data are galaxy clustering and weak lensing statistics (3x2pt) from the Dark Energy Survey (DES), cosmic microwave background (CMB) data from Planck, spectroscopic baryon acoustic oscillations (BAO) from the Dark Energy Spectroscopic Instrument (DESI), type-Ia supernovae (SNe Ia) samples from Pantheon+, and redshift-space distortions (RSD) from a collection of galaxy surveys. For each of these probes, we introduce a phenomenological split into these three regimes. This work shows a strong correlation between the geometric and the early regime for the matter density, but no strong correlation between the growth regime and the others. All regimes are compatible in the posterior distribution, however the difference between the geometry and the early regimes, $\Delta\Omega_{\rm m}^{\rm geo,early}$, is 2$\sigma$ apart from 0.

Figures

Figures reproduced from arXiv: 2607.28326 by Alain Blanchard, Felicitas Keil, Isaac Tutusaus.

Figure 1
Figure 1. Figure 1: Top: Split non-linear matter power spectrum at red [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Top: Split angular power spectrum of WL for the [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Top: The split two-point auto-correlation function [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The two-point correlation function ξ+(θ) for WL with DES Y3 data in the tomographic bin 4-4, including theoretical predictions with different Ωm values per regime. The DES Y3 data points are shown in grey and the grey band indicates the scale cuts. Bottom: Ratio of the split correlation function with respect to the non-split correla￾tion function with Ωm = 0.3. The cross-correlation between GC and WL is de… view at source ↗
Figure 7
Figure 7. Figure 7: All used fσ8 data points taken from the RSD mea￾surements compiled in Blanchard et al. (2024) in pink. The theory predictions are shown for different values of Ωm per regime. 4. Likelihood sampling To sample the parameter space, we use a modified version of CosmoSIS. The linear matter power spectrum is com￾puted with CAMB (Lewis et al. 2000; Howlett et al. 2012) and rescaled using Eq. (4). For the non-line… view at source ↗
Figure 9
Figure 9. Figure 9: 2D posterior distribution of Pantheon+ SNe Ia in [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 8
Figure 8. Figure 8: 2D posterior distribution of Pantheon+ SNe Ia in [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 10
Figure 10. Figure 10: Posterior distributions for all probes combined (Pantheon+, DES Y3, [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: 1D Posterior distributions of Ωm in the three regimes, Ω geo m in blue, Ω growth m in pink, and Ω early m in grey [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Posterior distribution of the difference between the [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗

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Reference graph

Works this paper leans on

150 extracted references · 2 canonical work pages

  1. [1]

    Testing gravity with CAMB and CosmoMC

    Hojjati, Alireza and Pogosian, Levon and Zhao, Gong-Bo. Testing gravity with CAMB and CosmoMC. JCAP. 2011. doi:10.1088/1475-7516/2011/08/005. arXiv:1106.4543

    Pith/arXiv arXiv 2011

  2. [2]

    A test of the standard cosmological model with geometry and growth

    Andrade, Uendert and Anbajagane, Dhayaa and von Marttens, Rodrigo and Huterer, Dragan and Alcaniz, Jailson. A test of the standard cosmological model with geometry and growth. JCAP. 2021. doi:10.1088/1475-7516/2021/11/014. arXiv:2107.07538

    Pith/arXiv arXiv 2021

  3. [3]

    Origin of cosmological neutrino mass bounds: background versus perturbations

    Bert \'o lez-Mart \' nez, Toni and Esteban, Ivan and Hajjar, Rasmi and Mena, Olga and Salvado, Jordi. Origin of cosmological neutrino mass bounds: background versus perturbations. JCAP. 2025. doi:10.1088/1475-7516/2025/06/058. arXiv:2411.14524

    Pith/arXiv arXiv 2025

  4. [4]

    The Three Faces of Omega \_ m: Testing Gravity with Low and High Redshift SN Ia Surveys

    Abate, Alexandra and Lahav, Ofer. The Three Faces of Omega \_ m: Testing Gravity with Low and High Redshift SN Ia Surveys. Mon. Not. Roy. Astron. Soc. 2008. doi:10.1111/j.1745-3933.2008.00519.x. arXiv:0805.3160

    arXiv 2008

  5. [5]

    Parameter splitting in dark energy: is dark energy the same in the background and in the cosmic structures?

    Bernal, Jos \'e Luis and Verde, Licia and Cuesta, Antonio J. Parameter splitting in dark energy: is dark energy the same in the background and in the cosmic structures?. JCAP. 2016. doi:10.1088/1475-7516/2016/02/059. arXiv:1511.03049

    Pith/arXiv arXiv 2016

  6. [6]

    and Eifler, Tim and Krause, Elisabeth

    Zhong, Kunhao and Saraivanov, Evan and Caputi, James and Miranda, Vivian and Boruah, Supranta S. and Eifler, Tim and Krause, Elisabeth. Attention-based neural network emulators for multiprobe data vectors. I. Forecasting the growth-geometry split. Phys. Rev. D. 2025. doi:10.1103/PhysRevD.111.123519. arXiv:2402.17716

    Pith/arXiv arXiv 2025

  7. [7]

    and Cuceu, Andrei and To, Chun-Hao and Zaborowski, Erik A

    Taylor, Peter L. and Cuceu, Andrei and To, Chun-Hao and Zaborowski, Erik A. CombineHarvesterFlow: Joint Probe Analysis Made Easy with Normalizing Flows. 2024. doi:10.33232/001c.124495. arXiv:2406.06687

    Pith/arXiv arXiv 2024

  8. [8]

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

    Ivezi \'c , Z eljko and others. LSST: from Science Drivers to Reference Design and Anticipated Data Products. Astrophys. J. 2019. doi:10.3847/1538-4357/ab042c. arXiv:0805.2366

    Pith/arXiv arXiv 2019

  9. [9]

    and others

    Friedrich, O. and others. Dark Energy Survey year 3 results: covariance modelling and its impact on parameter estimation and quality of fit. Mon. Not. Roy. Astron. Soc. 2021. doi:10.1093/mnras/stab2384. arXiv:2012.08568

    Pith/arXiv arXiv 2021

  10. [10]

    and others

    Krause, E. and others. Dark Energy Survey Year 3 Results: Multi-Probe Modeling Strategy and Validation. 2021. arXiv:2105.13548

    Pith/arXiv arXiv 2021

  11. [11]

    Tests of Evolving Dark Energy with Geometric Probes of the Late-Time Universe

    Zhong, Kunhao and Jain, Bhuvnesh. Tests of Evolving Dark Energy with Geometric Probes of the Late-Time Universe. 2025. arXiv:2509.26480

    arXiv 2025

  12. [12]

    The fallacies of LCDM falsifications

    Blanchard, Alain. The fallacies of LCDM falsifications. 2025. arXiv:2505.06244

    Pith/arXiv arXiv 2025

  13. [13]

    Challenges for CDM: An update

    Perivolaropoulos, Leandros and Skara, Foteini. Challenges for CDM: An update. New Astron. Rev. 2022. doi:10.1016/j.newar.2022.101659. arXiv:2105.05208

    arXiv 2022

  14. [14]

    Modern cosmology , isbn =

    Dodelson, Scott , year =. Modern cosmology , isbn =

  15. [15]

    and Cuceu, Andrei and To, Chun-Hao and Zaborowski, Erik A

    Taylor, Peter L. and Cuceu, Andrei and To, Chun-Hao and Zaborowski, Erik A. , journal =. CombineHarvesterFlow: Joint. doi:10.33232/001c.124495 , year =

    work page doi:10.33232/001c.124495

  16. [16]

    nautilus: boosting Bayesian importance nested sampling with deep learning

    Lange, Johannes U. nautilus: boosting Bayesian importance nested sampling with deep learning. Mon. Not. Roy. Astron. Soc. 2023. doi:10.1093/mnras/stad2441. arXiv:2306.16923

    Pith/arXiv arXiv 2023

  17. [17]

    and others

    Knabenhans, M. and others. Euclid preparation: IX. EuclidEmulator2 power spectrum emulation with massive neutrinos and self-consistent dark energy perturbations. Mon. Not. Roy. Astron. Soc. 2021. doi:10.1093/mnras/stab1366. arXiv:2010.11288

    Pith/arXiv arXiv 2021

  18. [18]

    A new perspective on Dark Energy modeling via Genetic Algorithms

    Nesseris, Savvas and Garcia-Bellido, Juan. A new perspective on Dark Energy modeling via Genetic Algorithms. JCAP. 2012. doi:10.1088/1475-7516/2012/11/033. arXiv:1205.0364

    Pith/arXiv arXiv 2012

  19. [19]

    Testing cosmological structure formation using redshift-space distortions

    Percival, Will J and White, Martin. Testing cosmological structure formation using redshift-space distortions. Mon. Not. Roy. Astron. Soc. 2009. doi:10.1111/j.1365-2966.2008.14211.x. arXiv:0808.0003

    arXiv 2009

  20. [20]

    and others

    Pandey, S. and others. Dark Energy Survey year 3 results: Constraints on cosmological parameters and galaxy-bias models from galaxy clustering and galaxy-galaxy lensing using the redMaGiC sample. Phys. Rev. D. 2022. doi:10.1103/PhysRevD.106.043520. arXiv:2105.13545

    Pith/arXiv arXiv 2022

  21. [21]

    Neutrino Masses, Scale-Dependent Growth, and Redshift-Space Distortions

    Hern \'a ndez, Oscar F. Neutrino Masses, Scale-Dependent Growth, and Redshift-Space Distortions. JCAP. 2017. doi:10.1088/1475-7516/2017/06/018. arXiv:1608.08298

    Pith/arXiv arXiv 2017

  22. [22]

    Precision calculations of the cosmic shear power spectrum projection

    Kilbinger, Martin and others. Precision calculations of the cosmic shear power spectrum projection. Mon. Not. Roy. Astron. Soc. 2017. doi:10.1093/mnras/stx2082. arXiv:1702.05301

    Pith/arXiv arXiv 2017

  23. [23]

    and others

    Martinelli, M. and others. Euclid: Forecast constraints on the cosmic distance duality relation with complementary external probes. Astron. Astrophys. 2020. doi:10.1051/0004-6361/202039078. arXiv:2007.16153

    Pith/arXiv arXiv 2020

  24. [24]

    Machine learning improved fits of the sound horizon at the baryon drag epoch

    Aizpuru, Andoni and Arjona, Rub\'en and Nesseris, Savvas. Machine learning improved fits of the sound horizon at the baryon drag epoch. Phys. Rev. D. 2021. doi:10.1103/PhysRevD.104.043521. arXiv:2106.00428

    Pith/arXiv arXiv 2021

  25. [25]

    The Pantheon+ Analysis: Cosmological Constraints

    Brout, Dillon and others. The Pantheon+ Analysis: Cosmological Constraints. Astrophys. J. 2022. doi:10.3847/1538-4357/ac8e04. arXiv:2202.04077

    Pith/arXiv arXiv 2022

  26. [26]

    and others

    Conley, A. and others. Supernova Constraints and Systematic Uncertainties from the First 3 Years of the Supernova Legacy Survey. Astrophys. J. Suppl. 2011. doi:10.1088/0067-0049/192/1/1. arXiv:1104.1443

    Pith/arXiv arXiv 2011

  27. [27]

    The Pantheon+ Analysis: The Full Data Set and Light-curve Release

    Scolnic, Dan and others. The Pantheon+ Analysis: The Full Data Set and Light-curve Release. Astrophys. J. 2022. doi:10.3847/1538-4357/ac8b7a. arXiv:2112.03863

    Pith/arXiv arXiv 2022

  28. [28]

    and others

    Nesseris, S. and others. Euclid: Forecast constraints on consistency tests of the CDM model. Astron. Astrophys. 2022. doi:10.1051/0004-6361/202142503. arXiv:2110.11421

    Pith/arXiv arXiv 2022

  29. [29]

    and Gomes, Mikael J

    Jesus, Jos\'e F. and Gomes, Mikael J. S. and Holanda, Rodrigo F. L. and Nunes, Rafael C. High-redshift cosmography with a possible cosmic distance duality relation violation. JCAP. 2025. doi:10.1088/1475-7516/2025/01/088. arXiv:2408.13390

    Pith/arXiv arXiv 2025

  30. [30]

    New tests of cosmic distance duality relation with DESI 2024 BAO observations

    Wang, Qiumin and Cao, Shuo and Jiang, Jianyong and Zhang, Kaituo and Jiang, Xinyue and Liu, Tonghua and Mu, Chengsheng and Cheng, Dadian. New tests of cosmic distance duality relation with DESI 2024 BAO observations. 2025. arXiv:2506.12759

    Pith/arXiv arXiv 2024

  31. [31]

    and Giar\`e, William and Hogg, Natalie B

    Teixeira, Elsa M. and Giar\`e, William and Hogg, Natalie B. and Montandon, Thomas and Poudou, Ad\`ele and Poulin, Vivian. Implications of distance duality violation for the H_0 tension and evolving dark energy. 2025. arXiv:2504.10464

    Pith/arXiv arXiv 2025

  32. [32]

    and Hu, Wayne

    Eisenstein, Daniel J. and Hu, Wayne. Baryonic features in the matter transfer function. Astrophys. J. 1998. doi:10.1086/305424. arXiv:astro-ph/9709112

    Pith/arXiv arXiv 1998

  33. [33]

    A Two-parameter luminosity correction for type Ia supernovae

    Tripp, Robert. A Two-parameter luminosity correction for type Ia supernovae. Astron. Astrophys. 1998

    1998

  34. [34]

    Constraints on cosmic opacity and beyond the standard model physics from cosmological distance measurements

    Avgoustidis, Anastasios and Burrage, Clare and Redondo, Javier and Verde, Licia and Jimenez, Raul. Constraints on cosmic opacity and beyond the standard model physics from cosmological distance measurements. JCAP. 2010. doi:10.1088/1475-7516/2010/10/024. arXiv:1004.2053

    Pith/arXiv arXiv 2010

  35. [35]

    Model-independent cosmological inference post DESI DR1 BAO measurements

    Mukherjee, Purba and Sen, Anjan Ananda. Model-independent cosmological inference post DESI DR1 BAO measurements. Phys. Rev. D. 2024. doi:10.1103/PhysRevD.110.123502. arXiv:2405.19178

    arXiv 2024

  36. [36]

    A Consistency Test of the Cosmological Model at the Epoch of Recombination Using DESI Baryonic Acoustic Oscillation and Planck Measurements

    Pogosian, Levon and Zhao, Gong-Bo and Jedamzik, Karsten. A Consistency Test of the Cosmological Model at the Epoch of Recombination Using DESI Baryonic Acoustic Oscillation and Planck Measurements. Astrophys. J. Lett. 2024. doi:10.3847/2041-8213/ad7507. arXiv:2405.20306

    Pith/arXiv arXiv 2024

  37. [37]

    Mixing of the Photon with Low Mass Particles

    Raffelt, Georg and Stodolsky, Leo. Mixing of the Photon with Low Mass Particles. Phys. Rev. D. 1988. doi:10.1103/PhysRevD.37.1237

    doi:10.1103/physrevd.37.1237 1988

  38. [38]

    The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample

    Alam, Shadab and others. The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample. Mon. Not. Roy. Astron. Soc. 2017. doi:10.1093/mnras/stx721. arXiv:1607.03155

    Pith/arXiv arXiv 2017

  39. [39]

    and Pettini, Max and Nollett, Kenneth M

    Cooke, Ryan J. and Pettini, Max and Nollett, Kenneth M. and Jorgenson, Regina. The primordial deuterium abundance of the most metal-poor damped Ly system. Astrophys. J. 2016. doi:10.3847/0004-637X/830/2/148. arXiv:1607.03900

    Pith/arXiv arXiv 2016

  40. [40]

    and others

    Dawson, Kyle S. and others. The SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Overview and Early Data. Astron. J. 2016. doi:10.3847/0004-6256/151/2/44. arXiv:1508.04473

    Pith/arXiv arXiv 2016

  41. [41]

    Scolnic, D. M. and others. The Complete Light-curve Sample of Spectroscopically Confirmed SNe Ia from Pan-STARRS1 and Cosmological Constraints from the Combined Pantheon Sample. Astrophys. J. 2018. doi:10.3847/1538-4357/aab9bb. arXiv:1710.00845

    Pith/arXiv arXiv 2018

  42. [42]

    Exploring the expansion history of the universe

    Linder, Eric V. Exploring the expansion history of the universe. Phys. Rev. Lett. 2003. doi:10.1103/PhysRevLett.90.091301. arXiv:astro-ph/0208512

    Pith/arXiv arXiv 2003

  43. [43]

    Accelerating universes with scaling dark matter

    Chevallier, Michel and Polarski, David. Accelerating universes with scaling dark matter. Int. J. Mod. Phys. D. 2001. doi:10.1142/S0218271801000822. arXiv:gr-qc/0009008

    Pith/arXiv arXiv 2001

  44. [44]

    oneberg, Nils , title =

    Sch\"oneberg, Nils , title = ". JCAP. 2024. doi:10.1088/1475-7516/2024/06/006. arXiv:2401.15054

    arXiv 2024

  45. [45]

    Testing the cosmic distance duality relation using Type Ia supernovae and BAO observations

    Yang, Fan and Fu, Xiangyun and Xu, Bing and Zhang, Kaituo and Huang, Yang and Yang, Ying. Testing the cosmic distance duality relation using Type Ia supernovae and BAO observations. Eur. Phys. J. C. 2025. doi:10.1140/epjc/s10052-025-13892-w. arXiv:2502.05417

    Pith/arXiv arXiv 2025

  46. [46]

    Lectures on cosmology : accelerated expansion of the Universe. 2010. doi:10.1007/978-3-642-10598-2

    work page doi:10.1007/978-3-642-10598-2 2010

  47. [47]

    Cosmic distance duality after DESI 2024 data release and dark energy evolution

    Alfano, Anna Chiara and Luongo, Orlando. Cosmic distance duality after DESI 2024 data release and dark energy evolution. 2025. arXiv:2501.15233

    Pith/arXiv arXiv 2024

  48. [48]

    Cosmic dissonance: are new physics or systematics behind a short sound horizon?

    Arendse, Nikki and others. Cosmic dissonance: are new physics or systematics behind a short sound horizon?. Astron. Astrophys. 2020. doi:10.1051/0004-6361/201936720. arXiv:1909.07986

    Pith/arXiv arXiv 2020

  49. [49]

    and Sheikh-Jabbari, M

    Colg \'a in, Eoin \'O . and Sheikh-Jabbari, M. M. DESI and SNe: Dynamical Dark Energy, _m Tension or Systematics?. Mon. Not. Roy. Astron. Soc. 2025. doi:10.1093/mnrasl/slaf042. arXiv:2412.12905

    Pith/arXiv arXiv 2025

  50. [50]

    and others

    Fern\'andez-Garc\' a, E. and others. Missing Components in CDM from DESI Y1 BAO Measurements: Insights from Redshift Remapping. 2025. arXiv:2503.22469

    arXiv 2025

  51. [51]

    and Sami, M

    Copeland, Edmund J. and Sami, M. and Tsujikawa, Shinji. Dynamics of dark energy. Int. J. Mod. Phys. D. 2006. doi:10.1142/S021827180600942X. arXiv:hep-th/0603057

    Pith/arXiv arXiv 2006

  52. [52]

    The Cosmological Constant Problem

    Weinberg, Steven. The Cosmological Constant Problem. Rev. Mod. Phys. 1989. doi:10.1103/RevModPhys.61.1

    doi:10.1103/revmodphys.61.1 1989

  53. [53]

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

    Asgari, Marika and others. KiDS-1000 Cosmology: Cosmic shear constraints and comparison between two point statistics. Astron. Astrophys. 2021. doi:10.1051/0004-6361/202039070. arXiv:2007.15633

    Pith/arXiv arXiv 2021

  54. [54]

    Cosmic acceleration vs axion - photon mixing

    Bassett, Bruce A. Cosmic acceleration vs axion - photon mixing. Astrophys. J. 2004. doi:10.1086/383520. arXiv:astro-ph/0311495

    Pith/arXiv arXiv 2004

  55. [55]

    oneberg, Nils and Franco Abell\'an, Guillermo and P\'erez S\'anchez, Andrea and Witte, Samuel J. and Poulin, Vivian and Lesgourgues, Julien , title =

    Sch\"oneberg, Nils and Franco Abell\'an, Guillermo and P\'erez S\'anchez, Andrea and Witte, Samuel J. and Poulin, Vivian and Lesgourgues, Julien , title = ". Phys. Rept. 2022. doi:10.1016/j.physrep.2022.07.001. arXiv:2107.10291

    Pith/arXiv arXiv 2022

  56. [56]

    Cosmology

    Weinberg, Steven. Cosmology. 2008

    2008

  57. [57]

    Weak lensing of the CMB

    Hanson, Duncan and Challinor, Anthony and Lewis, Antony. Weak lensing of the CMB. Gen. Rel. Grav. 2010. doi:10.1007/s10714-010-1036-y. arXiv:0911.0612

    Pith/arXiv arXiv 2010

  58. [58]

    Neutrino decoupling including flavour oscillations and primordial nucleosynthesis

    Froustey, Julien and Pitrou, Cyril and Volpe, Maria Cristina. Neutrino decoupling including flavour oscillations and primordial nucleosynthesis. JCAP. 2020. doi:10.1088/1475-7516/2020/12/015. arXiv:2008.01074

    Pith/arXiv arXiv 2020

  59. [59]

    Karhunen-Loeve eigenvalue problems in cosmology: How should we tackle large data sets?

    Tegmark, Max and Taylor, Andy and Heavens, Alan. Karhunen-Loeve eigenvalue problems in cosmology: How should we tackle large data sets?. Astrophys. J. 1997. doi:10.1086/303939. arXiv:astro-ph/9603021

    Pith/arXiv arXiv 1997

  60. [61]

    and others

    Suzuki, N. and others. The Hubble Space Telescope Cluster Supernova Survey: V. Improving the Dark Energy Constraints Above z > 1 and Building an Early-Type-Hosted Supernova Sample. Astrophys. J. 2012. doi:10.1088/0004-637X/746/1/85. arXiv:1105.3470

    Pith/arXiv arXiv 2012

  61. [62]

    Isolating Geometry in Weak Lensing Measurements

    Zhang, Jun and Hui, Lam and Stebbins, Albert. Isolating Geometry in Weak Lensing Measurements. Astrophys. J. 2005. doi:10.1086/497676. arXiv:astro-ph/0312348

    Pith/arXiv arXiv 2005

  62. [63]

    An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics

    Maus, Mark and Baleato Lizancos, Ant \'o n and White, Martin and de Mattia, Arnaud and Chen, Shi-Fan. An analytic approximation to the covariance between pre- and post-reconstruction galaxy two-point statistics. JCAP. 2026. doi:10.1088/1475-7516/2026/05/078. arXiv:2602.12343

    Pith/arXiv arXiv 2026

  63. [64]

    Cosmic distance duality relation in light of time-delayed strong gravitational lensing*

    Tang, Li and Lin, Hai-Nan and Wu, Ying. Cosmic distance duality relation in light of time-delayed strong gravitational lensing*. Chin. Phys. C. 2025. doi:10.1088/1674-1137/ad83a8. arXiv:2410.08595

    Pith/arXiv arXiv 2025

  64. [65]

    Testing the Cosmic Distance Duality Relation Using Strong Gravitational Lensing Time Delays and Type Ia Supernovae

    Qi, Jing-Zhao and Jiang, Yi-Fan and Hou, Wan-Ting and Zhang, Xin. Testing the Cosmic Distance Duality Relation Using Strong Gravitational Lensing Time Delays and Type Ia Supernovae. Astrophys. J. 2025. doi:10.3847/1538-4357/ad9de4. arXiv:2407.07336

    Pith/arXiv arXiv 2025

  65. [66]

    Holanda, R. F. L. and Carvalho, J. C. and Alcaniz, J. S. Model-independent constraints on the cosmic opacity. JCAP. 2013. doi:10.1088/1475-7516/2013/04/027. arXiv:1207.1694

    Pith/arXiv arXiv 2013

  66. [67]

    Measuring the galaxy-mass and galaxy-dust correlations through magnification and reddening

    Menard, Brice and Scranton, Ryan and Fukugita, Masataka and Richards, Gordon. Measuring the galaxy-mass and galaxy-dust correlations through magnification and reddening. Mon. Not. Roy. Astron. Soc. 2010. doi:10.1111/j.1365-2966.2010.16486.x. arXiv:0902.4240

    arXiv 2010

  67. [68]

    Model Independent Probe of Cosmic Distance Duality Relation

    Gahlaut, Savita. Model Independent Probe of Cosmic Distance Duality Relation. Res. Astron. Astrophys. 2025. doi:10.1088/1674-4527/adae45. arXiv:2501.15086

    Pith/arXiv arXiv 2025

  68. [69]

    Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift

    Ioffe, Sergey and Szegedy, Christian. Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift. 2015. arXiv:1502.03167

    Pith/arXiv arXiv 2015

  69. [70]

    A tale of two (or more) h's

    Brieden, Samuel and Gil-Mar\' n, H\'ector and Verde, Licia. A tale of two (or more) h's. JCAP. 2023. doi:10.1088/1475-7516/2023/04/023. arXiv:2212.04522

    Pith/arXiv arXiv 2023

  70. [71]

    and Spiro, Susanna and Hook, Isobel and Scaramella, Roberto

    Cardone, Vincenzo F. and Spiro, Susanna and Hook, Isobel and Scaramella, Roberto. Testing the distance duality relation with present and future data. Phys. Rev. D. 2012. doi:10.1103/PhysRevD.85.123510. arXiv:1205.1908

    Pith/arXiv arXiv 2012

  71. [72]

    Confronting Lemaitre-Tolman-Bondi models with Observational Cosmology

    Garcia-Bellido, Juan and Haugboelle, Troels. Confronting Lemaitre-Tolman-Bondi models with Observational Cosmology. JCAP. 2008. doi:10.1088/1475-7516/2008/04/003. arXiv:0802.1523

    Pith/arXiv arXiv 2008

  72. [73]

    Clustering in real space and in redshift space

    Kaiser, N. Clustering in real space and in redshift space. Mon. Not. Roy. Astron. Soc. 1987. doi:10.1093/mnras/227.1.1

    doi:10.1093/mnras/227.1.1 1987

  73. [74]

    and Baldry, I

    Liske, J. and Baldry, I. K. and Driver, S. P. and Tuffs, R. J. and Alpaslan, M. and Andrae, E. and Brough, S. and Cluver, M. E. and Grootes, M. W. and Gunawardhana, M. L. P. and Kelvin, L. S. and Loveday, J. and Robotham, A. S. G. and Taylor, E. N. and Bamford, S. P. and Bland-Hawthorn, J. and Brown, M. J. I. and Drinkwater, M. J. and Hopkins, A. M. and M...

    2015

  74. [75]

    and Hearin, Andrew P

    Lange, Johannes U. and Hearin, Andrew P. and Leauthaud, Alexie and van den Bosch, Frank C. and Guo, Hong and DeRose, Joseph. Five per \, cent measurements of the growth rate from simulation-based modelling of redshift-space clustering in BOSS LOWZ. Mon. Not. Roy. Astron. Soc. 2021. doi:10.1093/mnras/stab3111. arXiv:2101.12261

    Pith/arXiv arXiv 2021

  75. [76]

    Gil-Mar \' n, H \'e ctor and others. The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: structure growth rate measurement from the anisotropic quasar power spectrum in the redshift range 0.8 < z < 2.2. Mon. Not. Roy. Astron. Soc. 2018. doi:10.1093/mnras/sty453. arXiv:1801.02689

    Pith/arXiv arXiv 2018

  76. [78]

    The Subaru FMOS galaxy redshift survey (FastSound)

    Okumura, Teppei and others. The Subaru FMOS galaxy redshift survey (FastSound). IV. New constraint on gravity theory from redshift space distortions at z 1.4. Publ. Astron. Soc. Jap. 2016. doi:10.1093/pasj/psw029. arXiv:1511.08083

    Pith/arXiv arXiv 2016

  77. [79]

    and others

    de la Torre, S. and others. The VIMOS Public Extragalactic Redshift Survey (VIPERS). Gravity test from the combination of redshift-space distortions and galaxy-galaxy lensing at 0.5 < z < 1.2. Astron. Astrophys. 2017. doi:10.1051/0004-6361/201630276. arXiv:1612.05647

    Pith/arXiv arXiv 2017

  78. [80]

    and Myrzakulov, N

    Koussour, M. and Myrzakulov, N. and Alfedeel, Alnadhief H. A. and Abebe, Amare. Constraining the cosmological model of modified f(Q) gravity: Phantom dark energy and observational insights. PTEP. 2023. doi:10.1093/ptep/ptad133. arXiv:2310.15067

    Pith/arXiv arXiv 2023

  79. [81]

    Crossing the Phantom Divide

    Kunz, Martin and Sapone, Domenico. Crossing the Phantom Divide. Phys. Rev. D. 2006. doi:10.1103/PhysRevD.74.123503. arXiv:astro-ph/0609040

    Pith/arXiv arXiv 2006

  80. [82]

    and Hoffman, Mark and Trodden, Mark

    Carroll, Sean M. and Hoffman, Mark and Trodden, Mark. Can the dark energy equation-of-state parameter w be less than −1 ?. Phys. Rev. D. 2003. doi:10.1103/PhysRevD.68.023509. arXiv:astro-ph/0301273

    Pith/arXiv arXiv 2003

Showing first 80 references.