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A low-redshift test of structure growth finds S8 consistent with Planck but a 2.8-sigma low matter density.

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2026-08-04 10:26 UTC pith:6DDA2D5R

load-bearing objection Solid low-z growth measurement with a careful robustness analysis, but the 2.8σ low-Ωm headline softens to ~1σ under the paper's own alternative bias model. the 2 major comments →

arxiv 2510.09563 v2 pith:6DDA2D5R submitted 2025-10-10 astro-ph.CO

Low-redshift constraints on structure growth from CMB lensing tomography

Andrea Rubiola , Matteo Zennaro , Carlos Garc\'ia-Garc\'ia , David Alonso , Raul Angulo This is my paper
classification astro-ph.CO
keywords S8structure growthCMB lensing tomographygalaxy clusteringhybrid effective field theorylow redshiftmatter densityBAO prior
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.

This paper targets the least-explored epoch for structure-growth measurements: redshifts below about 0.3, where dark energy dominates the expansion and where late-time deviations in the growth of matter fluctuations would be most visible. Combining the projected clustering of three low-redshift galaxy samples with their cross-correlation against CMB lensing, and modelling galaxy bias with a hybrid effective field theory valid on mildly non-linear scales, the authors try to measure the growth amplitude S8 without relying on higher-redshift probes. With a BAO prior on the matter density they find S8=0.79±0.06, consistent with Planck and with other lensing tomography analyses. Without that prior, the data prefer Ωm=0.245±0.024, 2.8σ below Planck, a preference driven by the broadband shape of the highest-redshift galaxy auto-correlation and flagged as potentially sensitive to theoretical uncertainties in the bias templates. The low-redshift growth history they reconstruct is compatible with Planck, with a weak hint of steeper growth at the lowest redshifts.

Core claim

The central claim is that CMB lensing tomography at z≲0.3 can constrain the amplitude of matter fluctuations well enough to test Planck's growth prediction, provided the galaxy bias is modelled with a hybrid effective field theory. Using three low-redshift galaxy bins and CMB lensing from Planck, the paper reports S8=0.79±0.06 (with a BAO prior on Ωm) and σ8=0.80±0.06, both in agreement with Planck; when Ωm is left free, the data prefer Ωm=0.245±0.024, a 2.8σ disagreement. It further reconstructs σ8(z) at z≈0.07, 0.18 and 0.30, finding values compatible with Planck, and shows that the inferred HEFT bias parameters sit within 1σ of coevolution relations calibrated on galaxy formation simulati

What carries the argument

The load-bearing machinery is the hybrid effective field theory (HEFT) bias expansion, which writes the galaxy overdensity as an advected combination of the linear density, its square, the tidal field, and a derivative operator, with free bias coefficients; the operator cross-spectra come from an N-body emulator valid up to k≲0.6 h/Mpc. To go outside the emulator's training range in Ωm, the paper extrapolates the ratio of each operator spectrum to the matter spectrum using a first-order Taylor expansion, which introduces up to about 4% error near the BAO scale. Around this model sits a pseudo-Cℓ likelihood with analytic Gaussian, connected non-Gaussian, shot-noise, and redshift-distribution

Load-bearing premise

The result rests on the HEFT power-spectrum templates remaining accurate when extrapolated in matter density down to Ωm≈0.245, a regime where the emulator was not trained and where the extrapolation error reaches roughly 4% near the BAO scale.

What would settle it

Retrain the HEFT operator templates on N-body simulations run at Ωm≈0.245 and re-fit the same data vector: if the preferred Ωm moves back toward 0.30, the 2.8σ low-density hint is a template artifact; if it stays near 0.245, the preference is robust.

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

If this is right

  • If correct, low-redshift structure growth is consistent with Planck's ΛCDM prediction, leaving little room for new physics in growth at z<0.3.
  • The low Ωm preference, if real, would add a new low-redshift large-scale-structure anomaly driven by the shape of the galaxy power spectrum rather than by the BAO standard ruler.
  • Full HEFT modelling out to k≈0.42 Mpc⁻¹ does not yield smaller σ8 errors than a linear bias model cut at k≈0.11 Mpc⁻¹, since the extra small-scale modes mostly pay for the freedom in bias parameters.
  • The per-bin σ8(z) values provide a growth-history anchor at z≈0.1–0.3 that can be combined with higher-redshift lensing tomography to map the full growth curve.
  • The inferred bias parameters support the coevolution relations between linear and higher-order bias, potentially justifying simulation-based priors in future low-redshift analyses.

Where Pith is reading between the lines

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

  • If the Ωm preference is physical rather than a template artifact, it would join other low-Ωm hints from cosmic shear and intermediate-redshift lensing tomography, pointing either to a subtle shape-calibration issue in projected clustering or to a real tension between the BAO ruler and the broadband power-spectrum shape.
  • The ~4% template extrapolation error near the BAO scale is of the same order as the shift that separates Ωm=0.245 from 0.30, so a direct N-body validation at low Ωm would settle whether the 2.8σ result is evidence or systematics.
  • The weak constraining power of the two lowest-redshift bins suggests that pushing lensing tomography deep into the dark-energy epoch will require magnification information, smaller physical scales, or higher-density samples rather than simply more sky area.

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

2 major / 4 minor

Summary. The paper presents low-redshift (z ≲ 0.3) measurements of galaxy auto-power spectra and galaxy–CMB lensing cross-power spectra using 2MPZ and WISE×SuperCOSMOS galaxies in three tomographic bins, combined with Planck CMB lensing. Galaxy bias is modeled with a hybrid effective field theory (HEFT) approach whose template spectra are taken from the BACCO N-body emulator. Within flat ΛCDM, the authors report S8 = 0.79 ± 0.06 when a DESI BAO prior is imposed on Ωm, in good agreement with Planck; when Ωm is left free they find Ωm = 0.245 ± 0.024, a 2.8σ departure from Planck, and S8 = 0.82 ± 0.07. They also reconstruct σ8(z) at three redshifts, compare bias parameters with coevolution relations, and test robustness to scale cuts, a linear bias model, p(z) uncertainties, and volume effects via analytic marginalization. Appendix A repeats the Ωm measurement with an empirical bias model to isolate shape information.

Significance. If the S8 result is correct, it is a useful independent confirmation of Planck-compatible growth at very low redshifts using a sophisticated bias model and a complementary data combination. The paper has real strengths: the S8 value is stable across several analysis choices, volume effects are treated explicitly through the AAM procedure, and the Appendix A empirical-bias reanalysis is a valuable internal cross-check that explicitly probes the origin of the Ωm preference. The main weakness is that the headline 2.8σ low-Ωm anomaly is not stable under a change of bias model: Appendix A itself reduces the significance to roughly 1.5σ. The paper is honest about the HEFT extrapolation caveat, but the abstract and conclusions still foreground the 2.8σ number, which overstates the robustness of that anomaly.

major comments (2)
  1. [§4.1, Table 2; Appendix A, Table 4] The abstract's headline claim that the data favour Ωm = 0.245 ± 0.024, 2.8σ below Planck, is not robust to the bias model. The empirical bias model of Eq. (A.1), applied to the same data, gives Ωm = 0.264 ± 0.035 for all bins (PTE 62%) and Ωm = 0.250 ± 0.036 for Bin 3, i.e. only ~1.5σ and ~1.8σ below Planck. Since Appendix A shows the Ωm constraint is driven by the broadband shape of the Bin 3 galaxy auto-spectrum, the smaller significance from a model that does not depend on HEFT operator templates should be reported alongside the fiducial HEFT number in the abstract and conclusions. The 2.8σ significance overstates the current robustness of the low-Ωm preference.
  2. [§3.4.2, Eqs. (3.13)–(3.15), Fig. 2] The free-Ωm posterior extends to Ωm ≈ 0.245, outside the baccoemu training range, and the first-order Taylor extrapolation of Rij shows up to ~4% errors at k ~ 0.1 Mpc^{-1}, precisely the BAO-scale shape that drives the Ωm preference. The paper acknowledges this in the abstract, but it does not propagate the extrapolation uncertainty into the Ωm constraint. I request either (i) explicit validation of the emulator at low Ωm, (ii) a systematic error term in the Ωm measurement, or (iii) removal of the 2.8σ significance claim from the abstract. Without one of these, the free-Ωm result should be described only as preliminary.
minor comments (4)
  1. [§5] There is a duplicated word in the sentence “various types of galaxies galaxies”; please fix.
  2. [Fig. 5] The caption states that black points and error bars mark the mean and 68% intervals. For the skewed posteriors shown, reporting the median or mode would be less sensitive to tails; please clarify or change the reported statistic.
  3. [Eqs. (3.7), (3.10)] The symbol N^{gg}_ℓ is used for the analytic shot-noise spectrum in Eq. (3.10) while ~N^{ab}_ℓ denotes the noise pseudo-spectrum in Eq. (3.7). Please distinguish these notations explicitly to avoid confusion.
  4. [References] Reference [68] appears as “ThBeyond-2pt Collaboration”; this is likely a typo for “The Beyond-2pt Collaboration”.

Circularity Check

0 steps flagged

No significant circularity: HEFT templates come from N-body simulations independent of the target data, and the low-Ωm preference is not forced by construction.

full rationale

The paper's derivation chain is self-contained in the relevant sense. The theoretical model uses Hybrid Effective Field Theory with Pij templates measured in the BACCO N-body simulations and accelerated by an emulator [48,51,52]. These templates are calibrated on simulations, not on the 2MPZ/WISE×SuperCOSMOS or Planck lensing data used in the likelihood, so the cosmological constraints are not equivalent to a fitted input relabeled as a prediction. The bias parameters are free nuisance parameters fitted to the data, but the quantities reported as constraints—S8, Ωm, σ8—are not definitions of the fitted parameters. The free-Ωm preference, Ωm=0.245±0.024, is driven by the broadband shape of the galaxy auto-spectrum; the paper explicitly tests this interpretation with a different, empirical bias model in Appendix A, which reproduces a low-Ωm value (0.264±0.035), showing that the preference is not an artifact of the HEFT parametrization. The self-citations to the BACCO/HEFT program, the AAM marginalization procedure, and the empirical bias model are to externally validated tools: N-body simulations, statistical methods, and a different bias model, none of which contains the 2MPZ/WIxSC data or the Planck lensing measurements as inputs. The abstract's caveat that the low-Ωm result 'may be affected by theoretical uncertainties in the HEFT power spectrum templates' is a modeling-robustness concern, not evidence that the derivation is circular. The BAO-prior S8 result uses an external DESI prior, and the growth reconstruction is a derived quantity from standard ΛCDM, not a redefinition of the input. I find no step where the claimed output reduces by construction to the input.

Axiom & Free-Parameter Ledger

4 free parameters · 8 axioms · 0 invented entities

The ledger separates the scientific targets (σ8, Ωm, S8) from the nuisance parameters. The only genuinely ad hoc ingredient is the first-order Taylor extrapolation of the HEFT emulator outside its training range (Section 3.4.2); all other inputs are standard operational choices, validated approximations, or external data products. No new physical entities are introduced.

free parameters (4)
  • b1,i, b2,i, bs,i, b∇2,i (i=1,2,3) = Posterior means not explicitly quoted; broad Gaussian priors N(0,5) for b1,b2,bs and N(0,10 Mpc²) for b∇2
    Twelve HEFT bias nuisance parameters entering Eq. 3.4; marginalized analytically via AAM for cosmology and explicitly sampled for bias inference.
  • ASN,i (residual shot-noise amplitude per bin) = Not quoted; marginalized with σ_SN=0.1 Gaussian prior
    Accounts for non-Poisson stochastic contributions to galaxy auto-spectra (Section 3.3, Eq. 3.10).
  • p(z) bin amplitudes = Not quoted; bootstrap covariance from DIR calibration
    Marginalized via Eq. 3.11; assumes Gaussian errors and no inter-bin covariance.
  • Mmin,i and M1,i (HOD parameters for cNG covariance) = Not quoted; fitted to each bin's auto-spectrum
    Used to estimate the connected non-Gaussian covariance; subdominant on scales used; α=1, M0=Mmin, σlnM=0.4 fixed.
axioms (8)
  • domain assumption Flat ΛCDM background metric used for distances, kernels, and growth factor (Section 3.1, Eq. 3.2).
    All inferences assume a cosmological constant; no w0-wa or modified-gravity growth model is tested, so the growth reconstruction is model-dependent.
  • standard math Limber approximation (Eq. 3.3) is valid for these projected spectra.
    Authors test this and find <2% effect on S8, so it is not load-bearing.
  • domain assumption The Lagrangian bias expansion truncated at second order (Eq. 3.4) with operators δ, δ², s², ∇²δ is sufficient for k<0.42 Mpc⁻¹.
    HEFT validation in refs [48-50,54,67,68] supports this; failure would bias b1 and S8.
  • ad hoc to paper First-order Taylor extrapolation of HEFT templates outside the baccoemu training range is accurate (Eqs. 3.13-3.15).
    Free-Ωm posteriors reach Ωm≈0.245 outside the emulator range; Fig. 2 shows up to ~4% deviations, and the paper treats the low-Ωm result as possibly affected by this.
  • domain assumption The analytical covariance (Eq. 3.9: iNKA Gaussian + halo-model cNG + analytic shot-noise and p(z) marginalization) describes the true error distribution.
    Mis-estimated covariance would rescale quoted errors and the significance of tensions.
  • domain assumption DIR-calibrated redshift distributions and bootstrap uncertainties are unbiased and have uncorrelated bin-to-bin errors (Section 2.1).
    N(z) errors propagate via Eq. 3.11; the authors assume no correlation between bins, which may be optimistic.
  • domain assumption Empirical bias model of Appendix A (Eq. A.1) is valid to k=0.3 Mpc⁻¹.
    Used to show the Ωm preference is not an artifact of HEFT; relies on ref. [94].
  • domain assumption Fixed auxiliary parameters (Ωb h², n_s, Ωm h³=0.09633) are correct.
    Values taken from Planck/DESI; varying neutrino mass within bounds changes results by <1%, so impact is small.

pith-pipeline@v1.3.0-alltime-deepseek · 24936 in / 18866 out tokens · 174127 ms · 2026-08-04T10:26:34.450706+00:00 · methodology

0 comments
read the original abstract

We present constraints on the amplitude of matter fluctuations from the clustering of galaxies and their cross-correlation with the gravitational lensing convergence of the cosmic microwave background (CMB), focusing on low redshifts ($z\lesssim0.3$), where potential deviations from a perfect cosmological constant dominating the growth of structure could be more prominent. Specifically, we make use of data from the 2MASS photometric survey (\tmpz) and the \wisc galaxy survey, in combination with CMB lensing data from \planck. Using a hybrid effective field theory (HEFT) approach to model galaxy bias we obtain constraints on the combination $S_8=\sigma_8\sqrt{\Omega_m/0.3}$, where $\sigma_8$ is the amplitude of matter fluctuations, and $\Omega_m$ is the non-relativistic matter fraction. Using a prior on $\Omega_m$ based on the baryon acoustic oscillation measurements of DESI, we find $S_8=0.79\pm0.06$, in reasonable agreement with CMB constraints. We also find that, in the absence of this prior, the data favours a value of $\Omega_m=0.245\pm0.024$, that is 2.8$\sigma$ lower than \planck. This result is driven by the broadband shape of the galaxy auto-correlation, and may be affected by theoretical uncertainties in the HEFT power spectrum templates. We further reconstruct the low-redshift growth history, finding it to be compatible with the \planck predictions, as well as existing constraints from lensing tomography. Finally, we study our constraints on the HEFT bias parameters of the galaxy samples studied, finding them to be in reasonable agreement with coevolution predictions.

discussion (0)

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Forward citations

Cited by 3 Pith papers

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

  1. Synergy between the gravitational potential decay rate and other structure growth probes in testing gravity

    astro-ph.CO 2026-06 conditional novelty 5.0

    Combining gravitational-potential decay-rate (DR) data with Σ8 and fσ8 growth measurements tightens modified-gravity parameter constraints by ~1.5–2×, with all results consistent with general relativity.

  2. Biased tracers, Hybrid Effective Field Theory and Modified Gravity

    astro-ph.CO 2026-06 unverdicted novelty 5.0

    Extends HEFT to f(R) gravity for loop-corrected biased power spectra and outlines emulator extensions from LambdaCDM codes.

  3. Synergy between the gravitational potential decay rate and other structure growth probes in testing gravity

    astro-ph.CO 2026-06 unverdicted novelty 4.0

    Tomographic DR data added to Σ8 + fσ8 tightens phenomenological MG parameters (μ0, Σ0, η0) and EFT α coefficients by factors of 1.5–2.

Reference graph

Works this paper leans on

95 extracted references · 87 linked inside Pith · cited by 2 Pith papers

  1. [1]

    Adelberger, B.R

    E.G. Adelberger, B.R. Heckel and A.E. Nelson,Tests of the Gravitational Inverse-Square Law, Annual Review of Nuclear and Particle Science53(2003) 77 [hep-ph/0307284]

    Pith/arXiv arXiv 2003

  2. [2]

    Ferreira and C

    P.G. Ferreira and C. Skordis,Linear growth rate of structure in parametrized post-Friedmannian universes, Phys. Rev. D81(2010) 104020 [1003.4231]

    Pith/arXiv arXiv 2010

  3. [3]

    Ferreira,Cosmological Tests of Gravity, ARA&A57(2019) 335 [1902.10503]

    P.G. Ferreira,Cosmological Tests of Gravity, ARA&A57(2019) 335 [1902.10503]

    Pith/arXiv arXiv 2019

  4. [4]

    Kaiser,Clustering in real space and in redshift space, MNRAS227(1987) 1

    N. Kaiser,Clustering in real space and in redshift space, MNRAS227(1987) 1

    1987

  5. [5]

    Howlett, A.S.G

    C. Howlett, A.S.G. Robotham, C.D.P. Lagos and A.G. Kim,Measuring the Growth Rate of Structure with Type IA Supernovae from LSST, ApJ847(2017) 128 [1708.08236]

    Pith/arXiv arXiv 2017

  6. [6]

    Stahl, T

    B.E. Stahl, T. de Jaeger, S.S. Boruah, W. Zheng, A.V. Filippenko and M.J. Hudson, – 24 – Peculiar-velocity cosmology with Types Ia and II supernovae, MNRAS505(2021) 2349 [2105.05185]

    Pith/arXiv arXiv 2021

  7. [7]

    Bartelmann,TOPICAL REVIEW Gravitational lensing,Classical and Quantum Gravity27 (2010) 233001 [1010.3829]

    M. Bartelmann,TOPICAL REVIEW Gravitational lensing,Classical and Quantum Gravity27 (2010) 233001 [1010.3829]

    Pith/arXiv arXiv 2010

  8. [8]

    Lewis and A

    A. Lewis and A. Challinor,Weak gravitational lensing of the CMB, Phys. Rep.429(2006) 1 [astro-ph/0601594]

    Pith/arXiv arXiv 2006

  9. [9]

    Ivanov, M

    M.M. Ivanov, M. Simonović and M. Zaldarriaga,Cosmological parameters from the BOSS galaxy power spectrum, J. Cosmology Astropart. Phys.2020(2020) 042 [1909.05277]

    Pith/arXiv arXiv 2020

  10. [10]

    Tröster, A.G

    T. Tröster, A.G. Sánchez, M. Asgari, C. Blake, M. Crocce, C. Heymans et al.,Cosmology from large-scale structure. ConstrainingΛCDM with BOSS, A&A633(2020) L10 [1909.11006]

    Pith/arXiv arXiv 2020

  11. [11]

    M.S. Madhavacheril,Assessing the growth of structure over cosmic time with cosmic microwave background lensing,Philosophical Transactions of the Royal Society of London Series A383 (2025) 20240025 [2411.08152]

    Pith/arXiv arXiv 2025

  12. [12]

    Miyatake, Y

    H. Miyatake, Y. Harikane, M. Ouchi, Y. Ono, N. Yamamoto, A.J. Nishizawa et al.,First Identification of a CMB Lensing Signal Produced by 1.5 Million Galaxies at z∼4 : Constraints on Matter Density Fluctuations at High Redshift, Phys. Rev. Lett.129(2022) 061301 [2103.15862]

    Pith/arXiv arXiv 2022

  13. [13]

    Piccirilli, G

    G. Piccirilli, G. Fabbian, D. Alonso, K. Storey-Fisher, J. Carron, A. Lewis et al.,Growth history and quasar bias evolution at z < 3 from Quaia, J. Cosmology Astropart. Phys.2024 (2024) 012 [2402.05761]

    Pith/arXiv arXiv 2024

  14. [14]

    Farren, A

    G.S. Farren, A. Krolewski, F.J. Qu, S. Ferraro, E. Calabrese, J. Dunkley et al.,Atacama Cosmology Telescope: Multiprobe cosmology with unWISE galaxies and ACT DR6 CMB lensing, Phys. Rev. D111(2025) 083516 [2409.02109]

    Pith/arXiv arXiv 2025

  15. [15]

    de Belsunce, A

    R. de Belsunce, A. Krolewski, S. Chiarenza, E. Chaussidon, S. Ferraro, B. Hadzhiyska et al., Cosmology from Planck CMB Lensing and DESI DR1 Quasar Tomography,arXiv e-prints (2025) arXiv:2506.22416 [2506.22416]

    Pith/arXiv arXiv 2025

  16. [16]

    Embil Villagra, G

    C. Embil Villagra, G. Farren, G. Fabbian, B. Bolliet, I. Abril-Cabezas, D. Alonso et al.,The Atacama Cosmology Telescope: High-redshift measurement of structure growth from the cross-correlation of Quaia quasars and CMB lensing from ACT DR6 and Planck PR4,arXiv e-prints(2025) arXiv:2507.08798 [2507.08798]

    Pith/arXiv arXiv 2025

  17. [17]

    Krolewski, S

    A. Krolewski, S. Ferraro and M. White,Cosmological constraints from unWISE and Planck CMB lensing tomography, J. Cosmology Astropart. Phys.2021(2021) 028 [2105.03421]

    Pith/arXiv arXiv 2021

  18. [18]

    García-García, J

    C. García-García, J. Ruiz-Zapatero, D. Alonso, E. Bellini, P.G. Ferreira, E.-M. Mueller et al., The growth of density perturbations in the last 10 billion years from tomographic large-scale structure data, J. Cosmology Astropart. Phys.2021(2021) 030 [2105.12108]

    Pith/arXiv arXiv 2021

  19. [19]

    Farren, A

    G.S. Farren, A. Krolewski, N. MacCrann, S. Ferraro, I. Abril-Cabezas, R. An et al.,The Atacama Cosmology Telescope: Cosmology from Cross-correlations of unWISE Galaxies and ACT DR6 CMB Lensing, ApJ966(2024) 157 [2309.05659]

    Pith/arXiv arXiv 2024

  20. [20]

    Pellejero Ibáñez, R.E

    M. Pellejero Ibáñez, R.E. Angulo and J.A. Peacock,Cosmological constraints from the full-shape galaxy power spectrum in SDSS-III BOSS using the BACCO hybrid Lagrangian bias emulator, MNRAS534(2024) 3595 [2407.07949]

    Pith/arXiv arXiv 2024

  21. [21]

    Harscouet, D

    L. Harscouet, D. Alonso, A. Nicola and A. Slosar,Constraints from CMB lensing tomography with projected bispectra,arXiv e-prints(2025) arXiv:2507.07968 [2507.07968]

    arXiv 2025

  22. [22]

    Bianchini and C.L

    F. Bianchini and C.L. Reichardt,Constraining Gravity at Large Scales with the 2MASS Photometric Redshift Catalog and Planck Lensing, ApJ862(2018) 81 [1801.03736]. – 25 –

    Pith/arXiv arXiv 2018

  23. [23]

    Peacock and M

    J.A. Peacock and M. Bilicki,Wide-area tomography of CMB lensing and the growth of cosmological density fluctuations, MNRAS481(2018) 1133 [1805.11525]

    Pith/arXiv arXiv 2018

  24. [24]

    Sailer, J

    N. Sailer, J. DeRose, S. Ferraro, S.-F. Chen, R. Zhou, M. White et al.,Evolution of structure growth during dark energy domination: Insights from the cross-correlation of DESI galaxies with CMB lensing and galaxy magnification, Phys. Rev. D111(2025) 103540 [2503.24385]

    Pith/arXiv arXiv 2025

  25. [25]

    Asgari, C.-A

    M. Asgari, C.-A. Lin, B. Joachimi, B. Giblin, C. Heymans, H. Hildebrandt et al.,KiDS-1000 cosmology: Cosmic shear constraints and comparison between two point statistics, A&A645 (2021) A104 [2007.15633]

    Pith/arXiv arXiv 2021

  26. [26]

    A. Amon, D. Gruen, M.A. Troxel, N. MacCrann, S. Dodelson, A. Choi et al.,Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to data calibration, Phys. Rev. D105(2022) 023514 [2105.13543]

    arXiv 2022

  27. [27]

    Secco, S

    L.F. Secco, S. Samuroff, E. Krause, B. Jain, J. Blazek, M. Raveri et al.,Dark Energy Survey Year 3 results: Cosmology from cosmic shear and robustness to modeling uncertainty, Phys. Rev. D105(2022) 023515 [2105.13544]

    Pith/arXiv arXiv 2022

  28. [28]

    Dalal, X

    R. Dalal, X. Li, A. Nicola, J. Zuntz, M.A. Strauss, S. Sugiyama et al.,Hyper Suprime-Cam Year 3 results: Cosmology from cosmic shear power spectra, Phys. Rev. D108(2023) 123519 [2304.00701]

    Pith/arXiv arXiv 2023

  29. [29]

    Wright, B

    A.H. Wright, B. Stölzner, M. Asgari, M. Bilicki, B. Giblin, C. Heymans et al.,KiDS-Legacy: Cosmological constraints from cosmic shear with the complete Kilo-Degree Survey,arXiv e-prints(2025) arXiv:2503.19441 [2503.19441]

    Pith/arXiv arXiv 2025

  30. [30]

    Abdul-Karim, J

    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, arXiv e-prints(2025) arXiv:2503.14738 [2503.14738]

    Pith/arXiv arXiv 2025

  31. [31]

    G. Gu, X. Wang, Y. Wang, G.-B. Zhao, L. Pogosian, K. Koyama et al.,Dynamical dark energy in light of the DESI DR2 baryonic acoustic oscillations measurements,Nature Astronomy (2025) [2504.06118]

    arXiv 2025

  32. [32]

    Bilicki, T.H

    M. Bilicki, T.H. Jarrett, J.A. Peacock, M.E. Cluver and L. Steward,Two Micron All Sky Survey Photometric Redshift Catalog: A Comprehensive Three-dimensional Census of the Whole Sky, ApJS210(2014) 9 [1311.5246]

    Pith/arXiv arXiv 2014

  33. [33]

    Bilicki, J.A

    M. Bilicki, J.A. Peacock, T.H. Jarrett, M.E. Cluver, N. Maddox, M.J.I. Brown et al.,WISE× SuperCOSMOS Photometric Redshift Catalog: 20 Million Galaxies over 3/pi Steradians, ApJS 225(2016) 5 [1607.01182]

    Pith/arXiv arXiv 2016

  34. [34]

    Balaguera-Antolínez, M

    A. Balaguera-Antolínez, M. Bilicki, E. Branchini and A. Postiglione,Extracting cosmological information from the angular power spectrum of the 2MASS Photometric Redshift catalogue, MNRAS476(2018) 1050 [1711.04583]

    Pith/arXiv arXiv 2018

  35. [35]

    Jarrett, T

    T.H. Jarrett, T. Chester, R. Cutri, S. Schneider, M. Skrutskie and J.P. Huchra,2MASS Extended Source Catalog: Overview and Algorithms, AJ119(2000) 2498 [astro-ph/0004318]

    Pith/arXiv arXiv 2000

  36. [36]

    Wright, P.R.M

    E.L. Wright, P.R.M. Eisenhardt, A.K. Mainzer, M.E. Ressler, R.M. Cutri, T. Jarrett et al., The Wide-field Infrared Survey Explorer (WISE): Mission Description and Initial On-orbit Performance, AJ140(2010) 1868 [1008.0031]

    Pith/arXiv arXiv 2010

  37. [37]

    Hambly, M.J

    N.C. Hambly, M.J. Irwin and H.T. MacGillivray,The SuperCOSMOS Sky Survey - II. Image detection, parametrization, classification and photometry, MNRAS326(2001) 1295 [astro-ph/0108290]

    Pith/arXiv arXiv 2001

  38. [38]

    Lima, C.E

    M. Lima, C.E. Cunha, H. Oyaizu, J. Frieman, H. Lin and E.S. Sheldon,Estimating the redshift distribution of photometric galaxy samples, MNRAS390(2008) 118 [0801.3822]. – 26 –

    Pith/arXiv arXiv 2008

  39. [39]

    Paopiamsap, D

    A. Paopiamsap, D. Alonso, D.J. Bartlett and M. Bilicki,Constraints on dark matter and astrophysics from tomographicγ-ray cross-correlations, Phys. Rev. D109(2024) 103517 [2307.14881]

    Pith/arXiv arXiv 2024

  40. [40]

    Koukoufilippas, D

    N. Koukoufilippas, D. Alonso, M. Bilicki and J.A. Peacock,Tomographic measurement of the intergalactic gas pressure through galaxy-tSZ cross-correlations, MNRAS491(2020) 5464 [1909.09102]

    Pith/arXiv arXiv 2020

  41. [41]

    Zaldarriaga and U

    M. Zaldarriaga and U. Seljak,Reconstructing projected matter density power spectrum from cosmic microwave background, Phys. Rev. D59(1999) 123507 [astro-ph/9810257]

    Pith/arXiv arXiv 1999

  42. [42]

    Aghanim, Y

    Planck Collaboration, N. Aghanim, Y. Akrami, M. Ashdown, J. Aumont, C. Baccigalupi et al., Planck 2018 results. VIII. Gravitational lensing, A&A641(2020) A8 [1807.06210]

    Pith/arXiv arXiv 2018

  43. [43]

    Alonso, J

    D. Alonso, J. Sanchez, A. Slosar and LSST Dark Energy Science Collaboration,A unified pseudo-Cℓ framework, MNRAS484(2019) 4127 [1809.09603]

    Pith/arXiv arXiv 2019

  44. [44]

    Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al., Planck 2015 results. XV. Gravitational lensing, A&A594(2016) A15 [1502.01591]

    Pith/arXiv arXiv 2015

  45. [45]

    Limber,The Analysis of Counts of the Extragalactic Nebulae in Terms of a Fluctuating Density Field.,APJ117(1953) 134

    D.N. Limber,The Analysis of Counts of the Extragalactic Nebulae in Terms of a Fluctuating Density Field.,APJ117(1953) 134

    1953

  46. [46]

    Matsubara,Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture, Phys

    T. Matsubara,Nonlinear perturbation theory with halo bias and redshift-space distortions via the Lagrangian picture, Phys. Rev. D78(2008) 083519 [0807.1733]

    Pith/arXiv arXiv 2008

  47. [47]

    Modi, S.-F

    C. Modi, S.-F. Chen and M. White,Simulations and symmetries, MNRAS492(2020) 5754 [1910.07097]

    Pith/arXiv arXiv 2020

  48. [48]

    Zennaro, R.E

    M. Zennaro, R.E. Angulo, M. Pellejero-Ibáñez, J. Stücker, S. Contreras and G. Aricò,The BACCO simulation project: biased tracers in real space, MNRAS524(2023) 2407 [2101.12187]

    Pith/arXiv arXiv 2023

  49. [49]

    Kokron, J

    N. Kokron, J. DeRose, S.-F. Chen, M. White and R.H. Wechsler,The cosmology dependence of galaxy clustering and lensing from a hybrid N-body-perturbation theory model, MNRAS505 (2021) 1422 [2101.11014]

    Pith/arXiv arXiv 2021

  50. [50]

    Hadzhiyska, C

    B. Hadzhiyska, C. García-García, D. Alonso, A. Nicola and A. Slosar,Hefty enhancement of cosmological constraints from the DES Y1 data using a hybrid effective field theory approach to galaxy bias, J. Cosmology Astropart. Phys.2021(2021) 020 [2103.09820]

    Pith/arXiv arXiv 2021

  51. [51]

    Angulo, M

    R.E. Angulo, M. Zennaro, S. Contreras, G. Aricò, M. Pellejero-Ibañez and J. Stücker,The BACCO simulation project: exploiting the full power of large-scale structure for cosmology, MNRAS507(2021) 5869 [2004.06245]

    Pith/arXiv arXiv 2021

  52. [52]

    Aricò, R.E

    G. Aricò, R.E. Angulo and M. Zennaro,Accelerating Large-Scale-Structure data analyses by emulating Boltzmann solvers and Lagrangian Perturbation Theory,arXiv e-prints(2021) arXiv:2104.14568 [2104.14568]

    Pith/arXiv arXiv 2021

  53. [53]

    Zennaro, R.E

    M. Zennaro, R.E. Angulo, S. Contreras, M. Pellejero-Ibáñez and F. Maion,Priors on Lagrangian bias parameters from galaxy formation modelling, MNRAS514(2022) 5443 [2110.05408]

    Pith/arXiv arXiv 2022

  54. [54]

    Nicola, B

    A. Nicola, B. Hadzhiyska, N. Findlay, C. García-García, D. Alonso, A. Slosar et al.,Galaxy bias in the era of LSST: perturbative bias expansions, J. Cosmology Astropart. Phys.2024 (2024) 015 [2307.03226]

    Pith/arXiv arXiv 2024

  55. [55]

    Pezzotta, C

    Euclid Collaboration, A. Pezzotta, C. Moretti, M. Zennaro, A. Moradinezhad Dizgah, M. Crocce et al.,Euclid preparation. XLI. Galaxy power spectrum modelling in real space, A&A 687(2024) A216 [2312.00679]

    arXiv 2024

  56. [56]

    Hivon, K.M

    E. Hivon, K.M. Górski, C.B. Netterfield, B.P. Crill, S. Prunet and F. Hansen,MASTER of the Cosmic Microwave Background Anisotropy Power Spectrum: A Fast Method for Statistical – 27 – Analysis of Large and Complex Cosmic Microwave Background Data Sets, ApJ567(2002) 2 [astro-ph/0105302]

    Pith/arXiv arXiv 2002

  57. [57]

    García-García, D

    C. García-García, D. Alonso and E. Bellini,Disconnected pseudo-Cl covariances for projected large-scale structure data, J. Cosmology Astropart. Phys.2019(2019) 043 [1906.11765]

    Pith/arXiv arXiv 2019

  58. [58]

    Nicola, C

    A. Nicola, C. García-García, D. Alonso, J. Dunkley, P.G. Ferreira, A. Slosar et al.,Cosmic shear power spectra in practice, J. Cosmology Astropart. Phys.2021(2021) 067 [2010.09717]

    Pith/arXiv arXiv 2021

  59. [59]

    Krause and T

    E. Krause and T. Eifler,cosmolike - cosmological likelihood analyses for photometric galaxy surveys, MNRAS470(2017) 2100 [1601.05779]

    Pith/arXiv arXiv 2017

  60. [60]

    Peacock and R.E

    J.A. Peacock and R.E. Smith,Halo occupation numbers and galaxy bias, MNRAS318(2000) 1144 [astro-ph/0005010]

    Pith/arXiv arXiv 2000

  61. [61]

    Zheng, A.A

    Z. Zheng, A.A. Berlind, D.H. Weinberg, A.J. Benson, C.M. Baugh, S. Cole et al.,Theoretical Models of the Halo Occupation Distribution: Separating Central and Satellite Galaxies, ApJ 633(2005) 791 [astro-ph/0408564]

    Pith/arXiv arXiv 2005

  62. [62]

    Nicola, D

    A. Nicola, D. Alonso, J. Sánchez, A. Slosar, H. Awan, A. Broussard et al.,Tomographic galaxy clustering with the Subaru Hyper Suprime-Cam first year public data release, J. Cosmology Astropart. Phys.2020(2020) 044 [1912.08209]

    Pith/arXiv arXiv 2020

  63. [63]

    Hadzhiyska, D

    B. Hadzhiyska, D. Alonso, A. Nicola and A. Slosar,Analytic marginalization of N(z) uncertainties in tomographic galaxy surveys, J. Cosmology Astropart. Phys.2020(2020) 056 [2007.14989]

    Pith/arXiv arXiv 2020

  64. [64]

    Ruiz-Zapatero, B

    J. Ruiz-Zapatero, B. Hadzhiyska, D. Alonso, P.G. Ferreira, C. García-García and A. Mootoovaloo,Analytical marginalization over photometric redshift uncertainties in cosmic shear analyses, MNRAS522(2023) 5037 [2301.11978]

    Pith/arXiv arXiv 2023

  65. [65]

    Hamimeche and A

    S. Hamimeche and A. Lewis,Likelihood analysis of CMB temperature and polarization power spectra, Phys. Rev. D77(2008) 103013 [0801.0554]

    Pith/arXiv arXiv 2008

  66. [66]

    White, R

    M. White, R. Zhou, J. DeRose, S. Ferraro, S.-F. Chen, N. Kokron et al.,Cosmological constraints from the tomographic cross-correlation of DESI Luminous Red Galaxies and Planck CMB lensing, J. Cosmology Astropart. Phys.2022(2022) 007 [2111.09898]

    Pith/arXiv arXiv 2022

  67. [67]

    Pellejero Ibañez, R.E

    M. Pellejero Ibañez, R.E. Angulo, M. Zennaro, J. Stücker, S. Contreras, G. Aricò et al.,The bacco simulation project: bacco hybrid Lagrangian bias expansion model in redshift space, MNRAS520(2023) 3725 [2207.06437]

    Pith/arXiv arXiv 2023

  68. [68]

    Krause, Y

    ThBeyond-2pt Collaboration, E. Krause, Y. Kobayashi, A.N. Salcedo, M.M. Ivanov, T. Abel et al.,A Parameter-masked Mock Data Challenge for Beyond-two-point Galaxy Clustering Statistics, ApJ990(2025) 99 [2405.02252]

    Pith/arXiv arXiv 2025

  69. [69]

    Takahashi, M

    R. Takahashi, M. Sato, T. Nishimichi, A. Taruya and M. Oguri,Revising the Halofit Model for the Nonlinear Matter Power Spectrum, ApJ761(2012) 152 [1208.2701]

    Pith/arXiv arXiv 2012

  70. [70]

    Eisenstein and W

    D.J. Eisenstein and W. Hu,Baryonic Features in the Matter Transfer Function, ApJ496 (1998) 605 [astro-ph/9709112]

    Pith/arXiv arXiv 1998

  71. [71]

    Hadzhiyska, K

    B. Hadzhiyska, K. Wolz, S. Azzoni, D. Alonso, C. García-García, J. Ruiz-Zapatero et al., Cosmology with 6 parameters in the Stage-IV era: efficient marginalisation over nuisance parameters,The Open Journal of Astrophysics6(2023) 23 [2301.11895]

    Pith/arXiv arXiv 2023

  72. [72]

    M. Maus, S. Chen, M. White, J. Aguilar, S. Ahlen, A. Aviles et al.,An analysis of parameter compression and Full-Modeling techniques with Velocileptors for DESI 2024 and beyond, J. Cosmology Astropart. Phys.2025(2025) 138 [2404.07312]

    Pith/arXiv arXiv 2024

  73. [73]

    Ivanov, C

    M.M. Ivanov, C. Cuesta-Lazaro, S. Mishra-Sharma, A. Obuljen and M.W. Toomey,Full-shape analysis with simulation-based priors: Constraints on single field inflation from BOSS, Phys. Rev. D110(2024) 063538 [2402.13310]. – 28 –

    Pith/arXiv arXiv 2024

  74. [74]

    Chen and M.M

    S.-F. Chen and M.M. Ivanov,Constraining Dynamical Dark Energy from Galaxy Clustering with Simulation-Based Priors,arXiv e-prints(2025) arXiv:2507.00118 [2507.00118]

    Pith/arXiv arXiv 2025

  75. [75]

    Tsedrik, P

    M. Tsedrik, P. Carrilho and C. Moretti,The simple way to measure evolving dark energy without prior-volume effects,arXiv e-prints(2025) arXiv:2509.09562 [2509.09562]

    Pith/arXiv arXiv 2025

  76. [76]

    Torrado and A

    J. Torrado and A. Lewis,Cobaya: code for Bayesian analysis of hierarchical physical models, J. Cosmology Astropart. Phys.2021(2021) 057 [2005.05290]

    Pith/arXiv arXiv 2021

  77. [77]

    Chisari, D

    N.E. Chisari, D. Alonso, E. Krause, C.D. Leonard, P. Bull, J. Neveu et al.,Core Cosmology Library: Precision Cosmological Predictions for LSST, ApJS242(2019) 2 [1812.05995]

    Pith/arXiv arXiv 2019

  78. [78]

    Sailer, J

    N. Sailer, J. Kim, S. Ferraro, M.S. Madhavacheril, M. White, I. Abril-Cabezas et al., Cosmological constraints from the cross-correlation of DESI Luminous Red Galaxies with CMB lensing from Planck PR4 and ACT DR6, J. Cosmology Astropart. Phys.2025(2025) 008 [2407.04607]

    Pith/arXiv arXiv 2025

  79. [79]

    Marques and A

    G.A. Marques and A. Bernui,Tomographic analyses of the CMB lensing and galaxy clustering to probe the linear structure growth, J. Cosmology Astropart. Phys.2020(2020) 052 [1908.04854]

    Pith/arXiv arXiv 2020

  80. [80]

    Lazeyras, C

    T. Lazeyras, C. Wagner, T. Baldauf and F. Schmidt,Precision measurement of the local bias of dark matter halos, J. Cosmology Astropart. Phys.2016(2016) 018 [1511.01096]

    Pith/arXiv arXiv 2016

Showing first 80 references.