Cosmology-dependent covariance in galaxy cluster number counts: consequences for parameter inference

Henrique C. N. Lettieri; Mariana Penna-Lima; Sandro D. P. Vitenti

arxiv: 2606.30459 · v1 · pith:JFPNRIB2new · submitted 2026-06-29 · 🌌 astro-ph.CO · astro-ph.IM

Cosmology-dependent covariance in galaxy cluster number counts: consequences for parameter inference

Henrique C. N. Lettieri , Mariana Penna-Lima , Sandro D. P. Vitenti This is my paper

Pith reviewed 2026-06-30 04:48 UTC · model grok-4.3

classification 🌌 astro-ph.CO astro-ph.IM

keywords galaxy clustersnumber countscovariance matrixsuper-sample covariancecosmological parametersLSST survey

0 comments

The pith

Fixing the covariance at a displaced cosmology leaves cluster-count parameter estimates unbiased but distorts their uncertainties.

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

The paper tests what happens when the covariance matrix used in the likelihood for galaxy-cluster number counts is computed at the wrong cosmology instead of being updated at each sampled point. It finds that the recovered central values of Ω_c, σ_8, and w stay correct, yet the reported error bars can be too large or too small. The size and direction of the distortion are controlled mainly by amplitude parameters such as S_8, which can therefore alter the apparent tension between cluster data and other probes. A single recomputation of the covariance at the best-fit cosmology restores the proper uncertainty size without requiring continuous updates.

Core claim

Galaxy-cluster abundance analyses return unbiased estimates of Ω_c, σ_8, and w even when the full covariance (Poisson shot noise plus super-sample covariance) is evaluated at an incorrect cosmology. However, holding the covariance fixed at a displaced model over- or underestimates the confidence regions, with the effect driven primarily by amplitude-related parameters such as S_8. For LSST-like surveys a single covariance update performed at the recovered best-fit cosmology is sufficient to recover the correct uncertainty normalization.

What carries the argument

The cosmology-dependent covariance matrix for cluster counts, built from Poisson noise and super-sample covariance induced by long-wavelength density fluctuations, and its role inside the likelihood when either held fixed or recomputed consistently with the sampled parameters.

If this is right

Cluster-count constraints on S_8 can appear artificially tightened or loosened depending on the cosmology chosen for a fixed covariance.
Single-probe analyses may tolerate a fixed covariance if only central values are needed, but joint multi-probe studies require consistent cosmology dependence to avoid mismatched uncertainty estimates.
One covariance evaluation at the best-fit point suffices to correct the normalization, suggesting that full per-step updates are unnecessary for this observable.

Where Pith is reading between the lines

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

Iterative schemes that recompute covariance only at the current best-fit after each chain segment could be computationally efficient for large surveys.
The same fixed-covariance bias may appear when combining cluster counts with weak-lensing or CMB data, potentially shifting the joint posterior width without shifting the peak.

Load-bearing premise

The covariance, including its super-sample component, can be recomputed accurately at any displaced cosmology and the modeled mass-proxy scatter and photometric-redshift errors adequately represent LSST-like observations.

What would settle it

Generate mock cluster catalogs from a known input cosmology, run the same inference pipeline once with fixed covariance at a displaced point and once with cosmology-dependent covariance, then check whether the reported credible intervals match the actual scatter of recovered parameters across many realizations.

read the original abstract

Galaxy clusters provide constraints on cosmology through their abundance as a function of mass and redshift. Parameter inference from cluster counts requires modelling the covariance entering the likelihood, including contributions from Poisson shot noise and super-sample covariance (SSC) induced by long-wavelength density fluctuations. Since evaluating the full covariance during parameter inference can be computationally expensive, particularly for SSC terms, many analyses compute it at a fiducial cosmology and keep it fixed. In this work, we investigate the impact of covariance misspecification on the estimation of $\Omega_c$, $\sigma_8$, and $w$. We perform a systematic analysis in which the covariance is either varied consistently with the sampled cosmology or fixed at displaced cosmological models, including intermediate strategies where only selected components, such as SSC, are held fixed. Our analysis incorporates observational effects relevant for LSST-like optical surveys, including mass-proxy scatter and photometric redshift uncertainties. We find that the estimators of $\Omega_c$, $\sigma_8$, and $w$ remain unbiased even when the covariance is evaluated at an incorrect cosmology. However, fixing the covariance can significantly over- or underestimate confidence regions. The magnitude and sign of this effect are driven primarily by amplitude-related parameters such as $S_8$. For LSST-like surveys, an inconsistent covariance specification can artificially modify the apparent $S_8$ tension inferred from cluster counts. We further show that a single covariance update evaluated at the recovered best-fit cosmology is sufficient to restore the correct uncertainty normalization. These results indicate that fixed-covariance approximations may be adequate for some single-probe analyses, but a fully cosmology-dependent treatment is required for consistent multi-probe studies. ABRIDGED

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.

Desk Editor's Note private letter to a colleague

Fixed covariance leaves cluster-count central values unbiased but distorts error bars, especially for S8, and one update at the best-fit point restores the right normalization.

read the letter

The main thing to know is that this paper tests a practical approximation in cluster abundance work and finds the central estimates of Ωc, σ8, and w stay unbiased even when the covariance is evaluated at the wrong cosmology. What changes is the size of the reported uncertainties, and the distortion tracks amplitude parameters like S8. They also show that recomputing the covariance once at the recovered best-fit point is enough to fix the normalization.

They do a clean numerical comparison: full cosmology-dependent covariance versus fixed at displaced points, plus intermediate cases where only SSC is held fixed. The setup includes mass-proxy scatter and photometric redshift errors meant to mimic LSST-like data. That inclusion of observational systematics is the useful part; many earlier tests skipped them.

The soft spots are modest but real. The results rest on their ability to recompute the full covariance (including SSC) consistently at each cosmology, and the paper does not appear to include extensive cross-checks of that modeling against independent simulations. The S8-tension remark is stated but not demonstrated in a joint multi-probe run, so it remains suggestive. Because everything is numerical, the size of the effect will depend on the specific survey volume, mass range, and likelihood details they chose.

This is for people who actually run cluster-count likelihoods or are designing the covariance treatment for LSST/Euclid analyses. A reader who needs to decide whether to keep the covariance fixed or update it will get concrete guidance. The work is not proposing a new method, but the systematic test with systematics included is worth referee time. I would send it to review.

Referee Report

1 major / 0 minor

Summary. The paper performs a systematic numerical study of galaxy cluster number counts for LSST-like surveys, comparing parameter inference when the full covariance (including SSC) is varied consistently with the sampled cosmology versus held fixed at displaced models. It reports that estimators of Ω_c, σ_8, and w remain unbiased under covariance misspecification, but that fixed-covariance choices can over- or underestimate confidence regions (driven mainly by amplitude parameters such as S_8), with a single covariance update at the recovered best-fit cosmology sufficient to restore correct normalization. The work concludes that fixed-covariance approximations may suffice for some single-probe analyses but are inadequate for consistent multi-probe studies.

Significance. If the numerical results hold, the findings provide concrete guidance on covariance handling in cluster cosmology, with direct relevance to assessments of S_8 tension and to the design of multi-probe analyses. The systematic comparison of covariance strategies (full variation, partial fixes, and single-update) and the incorporation of observational effects (mass-proxy scatter, photo-z uncertainties) constitute a practical strength of the work.

major comments (1)

[Methods] Methods section: the manuscript provides insufficient detail on the simulation setup, the numerical implementation and verification of the SSC terms at displaced cosmologies, and the precise data exclusion choices. These elements are load-bearing for the central claim that uncertainty normalization is restored by a single update, because the reported bias/variance results depend directly on the accuracy of those recomputations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive feedback. We address the single major comment below and will revise the manuscript to incorporate additional methodological details as requested.

read point-by-point responses

Referee: [Methods] Methods section: the manuscript provides insufficient detail on the simulation setup, the numerical implementation and verification of the SSC terms at displaced cosmologies, and the precise data exclusion choices. These elements are load-bearing for the central claim that uncertainty normalization is restored by a single update, because the reported bias/variance results depend directly on the accuracy of those recomputations.

Authors: We agree that the current Methods section would benefit from greater detail to ensure full reproducibility and to strengthen the support for the reported results on uncertainty normalization. In the revised manuscript we will expand this section to provide: (i) a complete description of the simulation setup, including the specific mock catalog generation pipeline, volume, resolution, and cosmological parameters sampled; (ii) explicit documentation of the numerical implementation of the SSC terms (including the relevant integrals, code references, and how the terms are recomputed at each displaced cosmology); (iii) verification procedures such as convergence tests, comparisons against analytic limits, and cross-checks with independent SSC implementations; and (iv) the precise data exclusion criteria (redshift and mass cuts, handling of photo-z and mass-proxy scatter). These additions will directly address the referee's concern without altering the scientific conclusions. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central results—that estimators for Ω_c, σ_8, and w remain unbiased under covariance misspecification while uncertainties can be mis-normalized—are obtained from direct numerical comparisons of multiple covariance treatments (fully cosmology-dependent vs. fixed at displaced points, including partial fixes for SSC) inside parameter inference runs on simulated LSST-like cluster counts. These outcomes are not obtained by re-expressing a fitted quantity as a prediction or by reducing any claimed derivation to self-citation; the analysis explicitly varies the covariance matrix consistently with the sampled cosmology and reports the resulting posterior shifts. No load-bearing step reduces by construction to an input that was itself fitted or defined within the same analysis.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, new entities, or ad-hoc axioms are stated beyond standard cosmological modeling assumptions for covariance terms.

axioms (1)

domain assumption Super-sample covariance is induced by long-wavelength density fluctuations
Invoked in the abstract when describing the covariance components that must be modeled.

pith-pipeline@v0.9.1-grok · 5844 in / 1357 out tokens · 55363 ms · 2026-06-30T04:48:50.577312+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

64 extracted references · 62 canonical work pages · 33 internal anchors

[1]

Cosmological Parameters from Observations of Galaxy Clusters

S.W. Allen, A.E. Evrard and A.B. Mantz,Cosmological Parameters from Observations of Galaxy Clusters, Annual Review of Astronomy and Astrophysics49(2011) 409 [1103.4829]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[2]

Formation of Galaxy Clusters

A.V. Kravtsov and S. Borgani,Formation of Galaxy Clusters,Annual Review of Astronomy and Astrophysics 50(2012) 353 [1205.5556]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[3]

Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al.,Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts,Astronomy & Astrophysics594(2016) A24 [1502.01597]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[4]

E. Lee, R. Battye and B. Bolliet,Cosmological inference from combining Planck and ACT cluster counts, Monthly Notices of the Royal Astronomical Society538(2025) 2768 [2403.19542]

work page arXiv 2025
[5]

The Observed Growth of Massive Galaxy Clusters I: Statistical Methods and Cosmological Constraints

A. Mantz, S.W. Allen, D. Rapetti and H. Ebeling,The observed growth of massive galaxy clusters - I. Statistical methods and cosmological constraints,Monthly Notices of the Royal Astronomical Society406 (2010) 1759 [0909.3098]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[6]

Cluster Cosmology Constraints from the 2500 deg$^2$ SPT-SZ Survey: Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble Space Telescope

S. Bocquet, J.P. Dietrich, T. Schrabback, L.E. Bleem, M. Klein, S.W. Allen et al.,Cluster Cosmology Constraints from the 2500 deg2 SPT-SZ Survey: Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble Space Telescope,The Astrophysical Journal878(2019) 55 [1812.01679]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[7]

I.-N. Chiu, M. Klein, J. Mohr and S. Bocquet,Cosmological constraints from galaxy clusters and groups in the eROSITA final equatorial depth survey,Monthly Notices of the Royal Astronomical Society522(2023) 1601 [2207.12429]

work page arXiv 2023
[8]

Ghirardini, E

V. Ghirardini, E. Bulbul, E. Artis, N. Clerc, C. Garrel, S. Grandis et al.,The SRG/eROSITA all-sky survey: Cosmology constraints from cluster abundances in the western Galactic hemisphere,Astronomy & Astrophysics689(2024) A298 [2402.08458]

work page arXiv 2024
[9]

Bocquet, S

S. Bocquet, S. Grandis, L.E. Bleem, M. Klein, J.J. Mohr, T. Schrabback et al.,SPT clusters with DES and HST weak lensing. II. Cosmological constraints from the abundance of massive halos,Physical Review D110 (2024) 083510 [2401.02075]

work page arXiv 2024
[10]

Cosmological Constraints from the SDSS maxBCG Cluster Catalog

E. Rozo, R.H. Wechsler, E.S. Rykoff, J.T. Annis, M.R. Becker, A.E. Evrard et al.,Cosmological Constraints from the Sloan Digital Sky Survey maxBCG Cluster Catalog,The Astrophysical Journal708(2010) 645 [0902.3702]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[11]

Costanzi, E

M. Costanzi, E. Rozo, M. Simet, Y. Zhang, A.E. Evrard, A. Mantz et al.,Methods for cluster cosmology and application to the SDSS in preparation for DES Year 1 release,Monthly Notices of the Royal Astronomical Society488(2019) 4779 [1810.09456]

work page arXiv 2019
[12]

Abbott, M

T.M.C. Abbott, M. Aguena, A. Alarcon, S. Allam, S. Allen, J. Annis et al.,Dark Energy Survey Year 1 Results: Cosmological constraints from cluster abundances and weak lensing,Physical Review D102(2020) 023509 [2002.11124]. – 31 –

work page arXiv 2020
[13]

Abbott, M

T.M.C. Abbott, M. Aguena, A. Alarcon, A. Amon, D. Anbajagane, F. Andrade-Oliveira et al.,Dark energy surveyyear3results: Cosmologicalconstraintsfromclusterabundances,weaklensing,andgalaxyclustering, Physical Review D112(2025) 083535 [2503.13632]

work page arXiv 2025
[14]

Maturi, A

M. Maturi, A. Finoguenov, P.A.A. Lopes, R.M. González Delgado, R.A. Dupke, E.S. Cypriano et al.,The miniJPAS survey. Cluster and galaxy group detections with AMICO,Astronomy & Astrophysics678(2023) A145 [2307.06412]

work page arXiv 2023
[15]

Doubrawa, E.S

L. Doubrawa, E.S. Cypriano, A. Finoguenov, P.A.A. Lopes, A.H. Gonzalez, M. Maturi et al.,The miniJPAS survey. Optical detection of galaxy clusters with PZWav,Astronomy & Astrophysics685(2024) A98 [2312.12197]

work page arXiv 2024
[16]

LSST Dark Energy Science Collaboration,Large Synoptic Survey Telescope: Dark Energy Science Collaboration,arXiv e-prints(2012) arXiv:1211.0310 [1211.0310]

work page internal anchor Pith review Pith/arXiv arXiv 2012
[17]

Euclid Definition Study Report

R. Laureijs, J. Amiaux, S. Arduini, J.L. Auguères, J. Brinchmann, R. Cole et al.,Euclid Definition Study Report,arXiv e-prints(2011) arXiv:1110.3193 [1110.3193]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[18]

Artis, E

E. Artis, E. Bulbul, S. Grandis, V. Ghirardini, N. Clerc, R. Seppi et al.,The srg/erosita all-sky survey-constraints on the structure growth from cluster number counts,Astronomy & Astrophysics696(2025) A5 [2410.09499]

work page arXiv 2025
[19]

Sample Variance Considerations for Cluster Surveys

W. Hu and A.V. Kravtsov,Sample variance considerations for cluster surveys,The Astrophysical Journal584 (2003) 702 [astro-ph/0203169]

work page internal anchor Pith review Pith/arXiv arXiv 2003
[20]

Covariance matrices for halo number counts and correlation functions

P. Valageas, N. Clerc, F. Pacaud and M. Pierre,Covariance matrices for halo number counts and correlation functions,Astronomy & Astrophysics536(2011) A95 [1104.4015]

work page internal anchor Pith review Pith/arXiv arXiv 2011
[21]

M.TakadaandW.Hu,Powerspectrumsuper-samplecovariance,PhysicalReviewD87(2013) [1302.6994]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[22]

Joint analysis of cluster number counts and weak lensing power spectrum to correct for the super-sample covariance

M. Takada and D.N. Spergel,Joint analysis of cluster number counts and weak lensing power spectrum to correct for the super-sample covariance,Monthly Notices of the Royal Astronomical Society441(2014) 2456 [1307.4399]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[23]

Combining cluster number counts and galaxy clustering

F. Lacasa and R. Rosenfeld,Combining cluster number counts and galaxy clustering,Journal of Cosmology and Astroparticle Physics2016(2016) 005 [1603.00918]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[24]

Fast and easy super-sample covariance of large scale structure observables

F. Lacasa and J. Grain,Fast and easy super-sample covariance of large scale structure observables, Astronomy & Astrophysics624(2019) A61 [1809.05437]

work page internal anchor Pith review Pith/arXiv arXiv 2019
[25]

Gouyou Beauchamps, F

S. Gouyou Beauchamps, F. Lacasa, I. Tutusaus, M. Aubert, P. Baratta, A. Gorce et al.,Impact of survey geometry and super-sample covariance on future photometric galaxy surveys,Astronomy & Astrophysics659 (2022) A128 [2109.02308]

work page arXiv 2022
[26]

Super-sample covariance approximations and partial sky coverage

F. Lacasa, M. Lima and M. Aguena,Super-sample covariance approximations and partial sky coverage, Astronomy & Astrophysics611(2018) A83 [1612.05958]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[27]

Payerne, C

C. Payerne, C. Murray, C. Combet, C. Doux, A. Fumagalli and M. Penna-Lima,Testing the accuracy of likelihoods for cluster abundance cosmology,Monthly Notices of the Royal Astronomical Society520(2023) 6223 [2210.11093]

work page arXiv 2023
[28]

Payerne, C

C. Payerne, C. Murray, C. Combet and M. Penna-Lima,Towards including super-sample covariance in the unbinned likelihood for cluster abundance cosmology,Monthly Notices of the Royal Astronomical Society (2024) stae1504 [2401.10024]

work page arXiv 2024
[29]

Fumagalli, A

A. Fumagalli, A. Saro, S. Borgani, T. Castro, M. Costanzi, P. Monaco et al.,Euclid : Effects of sample covariance on the number counts of galaxy clusters,Astronomy & Astrophysics652(2021) A21 [2102.08914]

work page arXiv 2021
[30]

eROSITA cluster cosmology forecasts: cluster temperature substructure bias

F. Hofmann, J. Sanders, N. Clerc, K. Nandra, J. Ridl, K. Dennerl et al.,erosita cluster cosmology forecasts: Cluster temperature substructure bias,Astronomy & Astrophysics606(2017) A118 [1708.05205]. – 32 –

work page internal anchor Pith review Pith/arXiv arXiv 2017
[31]

Lacasa, M

F. Lacasa, M. Aubert, P. Baratta, J. Carron, A. Gorce, S.G. Beauchamps et al.,Efficient computation of the super-sample covariance for stage iv galaxy surveys,Astronomy & Astrophysics671(2023) A115 [2209.14421]

work page arXiv 2023
[32]

Ishida, S.D.P

E.E.O. Ishida, S.D.P. Vitenti, M. Penna-Lima, J. Cisewski, R.S. de Souza, A.M.M. Trindade et al., COSMOABC: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation, Astron. Comput.13(2015) 1 [1504.06129]

work page arXiv 2015
[33]

Í.Zubeldia,B.Bolliet,A.ChallinorandW.Handley,Extractingcosmologicalinformationfromtheabundance of galaxy clusters with simulation-based inference,Physical Review D112(2025) 083536 [2504.10230]

work page arXiv 2025
[34]

Cerardi, M

N. Cerardi, M. Pierre, F. Lanusse and X. Corap,The Cosmological analysis of X-ray cluster surveys: VII. Bypassing scaling relations with Lagrangian Deep Learning and Simulation-based inference,Astronomy & Astrophysics701(2025) A110 [2507.01820]

work page arXiv 2025
[35]

Ntampaka, A

M. Ntampaka, A. Ciprijanovic, A.M. Delgado, J. Soltis, J.F. Wu, M. Yunus et al.,The Importance of Being Adaptable: An Exploration of the Power and Limitations of Domain Adaptation for Simulation-Based Inference with Galaxy Clusters,arXiv e-prints(2025) arXiv:2510.09748 [2510.09748]

work page arXiv 2025
[36]

Simulation-based cosmological inference from optically-selected galaxy clusters with $\texttt{Capish}$

C. Payerne, C. Murray and H. Simon,Simulation-based cosmological inference from optically-selected galaxy clusters withCapish,arXiv e-prints(2026) arXiv:2602.01911 [2602.01911]

work page internal anchor Pith review Pith/arXiv arXiv 2026
[37]

J. Prat, J. Zuntz, C. Chang, T. Tröster, E. Pedersen, C. García-García et al.,The catalog-to-cosmology framework for weak lensing and galaxy clustering for lsst,The Open Journal of Astrophysics6(2023) [2212.09345]

work page arXiv 2023
[38]

Fumagalli, M

A. Fumagalli, M. Costanzi, A. Saro, T. Castro and S. Borgani,Cosmological constraints from the abundance, weak lensing, and clustering of galaxy clusters: Application to the SDSS,Astronomy & Astrophysics682 (2024) A148 [2310.09146]

work page arXiv 2024
[39]

Galaxy-galaxy weak lensing in SDSS: intrinsic alignments and shear calibration errors

C.M. Hirata, R. Mandelbaum, U. Seljak, J. Guzik, N. Padmanabhan, C. Blake et al.,Galaxy-galaxy weak lensing in the Sloan Digital Sky Survey: intrinsic alignments and shear calibration errors,Monthly Notices of the Royal Astronomical Society353(2004) 529 [astro-ph/0403255]

work page internal anchor Pith review Pith/arXiv arXiv 2004
[40]

Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix

J. Hartlap, P. Simon and P. Schneider,Why your model parameter confidences might be too optimistic. unbiased estimation of the inverse covariance matrix,Astronomy & Astrophysics464(2006) 399–404 [astro-ph/0608064]

work page internal anchor Pith review Pith/arXiv arXiv 2006
[41]

Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation

T. Eifler, P. Schneider and J. Hartlap,Dependence of cosmic shear covariances on cosmology-impact on parameter estimation,Astronomy & Astrophysics502(2009) 721 [0810.4254]

work page internal anchor Pith review Pith/arXiv arXiv 2009
[42]

Cosmological parameter constraints from galaxy-galaxy lensing and galaxy clustering with the SDSS DR7

R. Mandelbaum, A. Slosar, T. Baldauf, U. Seljak, C.M. Hirata, R. Nakajima et al.,Cosmological parameter constraints from galaxy-galaxy lensing and galaxy clustering with the SDSS DR7,Monthly Notices of the Royal Astronomical Society432(2013) 1544 [1207.1120]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[43]

CosmoLike - Cosmological Likelihood Analyses for Photometric Galaxy Surveys

E. Krause and T. Eifler,cosmolike – cosmological likelihood analyses for photometric galaxy surveys,Monthly Notices of the Royal Astronomical Society470(2017) 2100 [1601.05779]

work page internal anchor Pith review Pith/arXiv arXiv 2017
[44]

Precision matrix expansion - efficient use of numerical simulations in estimating errors on cosmological parameters

O. Friedrich and T. Eifler,Precision matrix expansion - efficient use of numerical simulations in estimating errors on cosmological parameters,Monthly Notices of the Royal Astronomical Society473(2018) 4150 [1703.07786]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[45]

The Effect of Covariance Estimator Error on Cosmological Parameter Constraints

S. Dodelson and M.D. Schneider,The effect of covariance estimator error on cosmological parameter constraints,Physical Review D88(2013) [1304.2593]

work page internal anchor Pith review Pith/arXiv arXiv 2013
[46]

Biases on cosmological parameter estimators from galaxy cluster number counts

M. Penna-Lima, M. Makler and C.A. Wuensche,Biases on cosmological parameter estimators from galaxy cluster number counts,Journal of Cosmology and Astroparticle Physics2014(2014) 039 [1312.4430]

work page internal anchor Pith review Pith/arXiv arXiv 2014
[47]

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

E. Abdalla, G.F. Abellán, A. Aboubrahim, A. Agnello, Ö. Akarsu, Y. Akrami et al.,Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies,Journal of High Energy Astrophysics34(2022) 49 [2203.06142]. – 33 –

work page internal anchor Pith review Pith/arXiv arXiv 2022
[48]

Pantos and L

I. Pantos and L. Perivolaropoulos,Status of the𝑆8 Tension: A 2026 Review of Probe Discrepancies,arXiv e-prints(2026) arXiv:2602.12238 [2602.12238]. [49]Planckcollaboration,Planck 2018 results. VI. Cosmological parameters,Astron. Astrophys.641(2020) A6 [1807.06209]

work page arXiv 2026
[49]

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,Astronomy & Astrophysics645(2021) A104 [2007.15633]

work page arXiv 2021
[50]

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,Physical Review D108(2023) 123519

2023
[51]

Sunayama, H

T. Sunayama, H. Miyatake, S. Sugiyama, S. More, X. Li, R. Dalal et al.,Optical cluster cosmology with SDSS redMaPPer clusters and HSC-Y3 lensing measurements,Physical Review D110(2024) 083511 [2309.13025]

work page arXiv 2024
[52]

Miyatake,Cosmology with Galaxy Clusters,arXiv e-prints(2025) arXiv:2505.07697 [2505.07697]

H. Miyatake,Cosmology with Galaxy Clusters,arXiv e-prints(2025) arXiv:2505.07697 [2505.07697]

work page arXiv 2025
[53]

NumCosmo: Numerical Cosmology

S. Dias Pinto Vitenti and M. Penna-Lima, “NumCosmo: Numerical Cosmology.” Astrophysics Source Code Library ascl:1408.013, Aug., 2014

2014
[54]

J.Tinker, A.V.Kravtsov, A.Klypin, K.Abazajian, M.Warren, G.Yepesetal.,Towardahalomassfunctionfor precision cosmology: The limits of universality,The Astrophysical Journal688(2008) 709 [0803.2706]

work page internal anchor Pith review Pith/arXiv arXiv 2008
[55]

The universality of the virial halo mass function and models for non-universality of other halo definitions

G. Despali, C. Giocoli, R.E. Angulo, G. Tormen, R.K. Sheth, G. Baso et al.,The universality of the virial halo mass function and models for non-universality of other halo definitions,Monthly Notices of the Royal Astronomical Society456(2016) 2486 [1507.05627]

work page internal anchor Pith review Pith/arXiv arXiv 2016
[56]

Semi-analytic predictions for statistical properties of X-ray clusters of galaxies in cold dark matter universes

T. Kitayama and Y. Suto,Semi-analytic predictions for statistical properties of x-ray clusters of galaxies in cold dark matter universes,The Astrophysical Journal469(1996) 480 [astro-ph/9604141]

work page internal anchor Pith review Pith/arXiv arXiv 1996
[57]

Baryonic Features in the Matter Transfer Function

D.J. Eisenstein and W. Hu,Baryonic features in the matter transfer function,The Astrophysical Journal496 (1998) 605 [astro-ph/9709112]

work page internal anchor Pith review Pith/arXiv arXiv 1998
[58]

Kaiser,On the spatial correlations of Abell clusters., vol

N. Kaiser,On the spatial correlations of Abell clusters., vol. 284 (1984), 10.1086/184341

work page doi:10.1086/184341 1984
[59]

An analytic model for the spatial clustering of dark matter haloes

H. Mo and S.D. White,An analytic model for the spatial clustering of dark matter haloes,Monthly Notices of the Royal Astronomical Society282(1996) 347 [astro-ph/9512127]

work page internal anchor Pith review Pith/arXiv arXiv 1996
[60]

The Large Scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests

J.L. Tinker, B.E. Robertson, A.V. Kravtsov, A. Klypin, M.S. Warren, G. Yepes et al.,The large-scale bias of dark matter halos: Numerical calibration and model tests,The Astrophysical Journal724(2010) 878 [1001.3162]

work page internal anchor Pith review Pith/arXiv arXiv 2010
[61]

Ishiyama et al.,The Uchuu simulations: Data Release 1 and dark matter halo concentrations,Monthly Notices of the Royal Astronomical Society506(2021) 4210 [2007.14720]

T. Ishiyama et al.,The Uchuu simulations: Data Release 1 and dark matter halo concentrations,Monthly Notices of the Royal Astronomical Society506(2021) 4210 [2007.14720]

work page arXiv 2021
[62]

Constraints on the mass-richness relation from the abundance and weak lensing of SDSS clusters

R. Murata, T. Nishimichi, M. Takada, H. Miyatake, M. Shirasaki, S. More et al.,Constraints on the mass–richness relation from the abundance and weak lensing of sdss clusters,The Astrophysical Journal854 (2018) 120 [1707.01907]

work page internal anchor Pith review Pith/arXiv arXiv 2018
[63]

Mandelbaum, T

R. Mandelbaum, T. Eifler, R. Hložek, T. Collett, E. Gawiser, D. Scolnic et al.,The lsst dark energy science collaboration(desc)sciencerequirementsdocument,arXivpreprintarXiv:1809.01669(2018) [1809.01669]

work page arXiv 2018
[64]

D P Vitenti and E.J

S. D P Vitenti and E.J. Barroso,Apes: approximate posterior ensemble sampler,Monthly Notices of the Royal Astronomical Society525(2023) 73 [2303.13667]. – 34 –

work page arXiv 2023

[1] [1]

Cosmological Parameters from Observations of Galaxy Clusters

S.W. Allen, A.E. Evrard and A.B. Mantz,Cosmological Parameters from Observations of Galaxy Clusters, Annual Review of Astronomy and Astrophysics49(2011) 409 [1103.4829]

work page internal anchor Pith review Pith/arXiv arXiv 2011

[2] [2]

Formation of Galaxy Clusters

A.V. Kravtsov and S. Borgani,Formation of Galaxy Clusters,Annual Review of Astronomy and Astrophysics 50(2012) 353 [1205.5556]

work page internal anchor Pith review Pith/arXiv arXiv 2012

[3] [3]

Planck Collaboration, P.A.R. Ade, N. Aghanim, M. Arnaud, M. Ashdown, J. Aumont et al.,Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts,Astronomy & Astrophysics594(2016) A24 [1502.01597]

work page internal anchor Pith review Pith/arXiv arXiv 2015

[4] [4]

E. Lee, R. Battye and B. Bolliet,Cosmological inference from combining Planck and ACT cluster counts, Monthly Notices of the Royal Astronomical Society538(2025) 2768 [2403.19542]

work page arXiv 2025

[5] [5]

The Observed Growth of Massive Galaxy Clusters I: Statistical Methods and Cosmological Constraints

A. Mantz, S.W. Allen, D. Rapetti and H. Ebeling,The observed growth of massive galaxy clusters - I. Statistical methods and cosmological constraints,Monthly Notices of the Royal Astronomical Society406 (2010) 1759 [0909.3098]

work page internal anchor Pith review Pith/arXiv arXiv 2010

[6] [6]

Cluster Cosmology Constraints from the 2500 deg$^2$ SPT-SZ Survey: Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble Space Telescope

S. Bocquet, J.P. Dietrich, T. Schrabback, L.E. Bleem, M. Klein, S.W. Allen et al.,Cluster Cosmology Constraints from the 2500 deg2 SPT-SZ Survey: Inclusion of Weak Gravitational Lensing Data from Magellan and the Hubble Space Telescope,The Astrophysical Journal878(2019) 55 [1812.01679]

work page internal anchor Pith review Pith/arXiv arXiv 2019

[7] [7]

I.-N. Chiu, M. Klein, J. Mohr and S. Bocquet,Cosmological constraints from galaxy clusters and groups in the eROSITA final equatorial depth survey,Monthly Notices of the Royal Astronomical Society522(2023) 1601 [2207.12429]

work page arXiv 2023

[8] [8]

Ghirardini, E

V. Ghirardini, E. Bulbul, E. Artis, N. Clerc, C. Garrel, S. Grandis et al.,The SRG/eROSITA all-sky survey: Cosmology constraints from cluster abundances in the western Galactic hemisphere,Astronomy & Astrophysics689(2024) A298 [2402.08458]

work page arXiv 2024

[9] [9]

Bocquet, S

S. Bocquet, S. Grandis, L.E. Bleem, M. Klein, J.J. Mohr, T. Schrabback et al.,SPT clusters with DES and HST weak lensing. II. Cosmological constraints from the abundance of massive halos,Physical Review D110 (2024) 083510 [2401.02075]

work page arXiv 2024

[10] [10]

Cosmological Constraints from the SDSS maxBCG Cluster Catalog

E. Rozo, R.H. Wechsler, E.S. Rykoff, J.T. Annis, M.R. Becker, A.E. Evrard et al.,Cosmological Constraints from the Sloan Digital Sky Survey maxBCG Cluster Catalog,The Astrophysical Journal708(2010) 645 [0902.3702]

work page internal anchor Pith review Pith/arXiv arXiv 2010

[11] [11]

Costanzi, E

M. Costanzi, E. Rozo, M. Simet, Y. Zhang, A.E. Evrard, A. Mantz et al.,Methods for cluster cosmology and application to the SDSS in preparation for DES Year 1 release,Monthly Notices of the Royal Astronomical Society488(2019) 4779 [1810.09456]

work page arXiv 2019

[12] [12]

Abbott, M

T.M.C. Abbott, M. Aguena, A. Alarcon, S. Allam, S. Allen, J. Annis et al.,Dark Energy Survey Year 1 Results: Cosmological constraints from cluster abundances and weak lensing,Physical Review D102(2020) 023509 [2002.11124]. – 31 –

work page arXiv 2020

[13] [13]

Abbott, M

T.M.C. Abbott, M. Aguena, A. Alarcon, A. Amon, D. Anbajagane, F. Andrade-Oliveira et al.,Dark energy surveyyear3results: Cosmologicalconstraintsfromclusterabundances,weaklensing,andgalaxyclustering, Physical Review D112(2025) 083535 [2503.13632]

work page arXiv 2025

[14] [14]

Maturi, A

M. Maturi, A. Finoguenov, P.A.A. Lopes, R.M. González Delgado, R.A. Dupke, E.S. Cypriano et al.,The miniJPAS survey. Cluster and galaxy group detections with AMICO,Astronomy & Astrophysics678(2023) A145 [2307.06412]

work page arXiv 2023

[15] [15]

Doubrawa, E.S

L. Doubrawa, E.S. Cypriano, A. Finoguenov, P.A.A. Lopes, A.H. Gonzalez, M. Maturi et al.,The miniJPAS survey. Optical detection of galaxy clusters with PZWav,Astronomy & Astrophysics685(2024) A98 [2312.12197]

work page arXiv 2024

[16] [16]

LSST Dark Energy Science Collaboration,Large Synoptic Survey Telescope: Dark Energy Science Collaboration,arXiv e-prints(2012) arXiv:1211.0310 [1211.0310]

work page internal anchor Pith review Pith/arXiv arXiv 2012

[17] [17]

Euclid Definition Study Report

R. Laureijs, J. Amiaux, S. Arduini, J.L. Auguères, J. Brinchmann, R. Cole et al.,Euclid Definition Study Report,arXiv e-prints(2011) arXiv:1110.3193 [1110.3193]

work page internal anchor Pith review Pith/arXiv arXiv 2011

[18] [18]

Artis, E

E. Artis, E. Bulbul, S. Grandis, V. Ghirardini, N. Clerc, R. Seppi et al.,The srg/erosita all-sky survey-constraints on the structure growth from cluster number counts,Astronomy & Astrophysics696(2025) A5 [2410.09499]

work page arXiv 2025

[19] [19]

Sample Variance Considerations for Cluster Surveys

W. Hu and A.V. Kravtsov,Sample variance considerations for cluster surveys,The Astrophysical Journal584 (2003) 702 [astro-ph/0203169]

work page internal anchor Pith review Pith/arXiv arXiv 2003

[20] [20]

Covariance matrices for halo number counts and correlation functions

P. Valageas, N. Clerc, F. Pacaud and M. Pierre,Covariance matrices for halo number counts and correlation functions,Astronomy & Astrophysics536(2011) A95 [1104.4015]

work page internal anchor Pith review Pith/arXiv arXiv 2011

[21] [21]

M.TakadaandW.Hu,Powerspectrumsuper-samplecovariance,PhysicalReviewD87(2013) [1302.6994]

work page internal anchor Pith review Pith/arXiv arXiv 2013

[22] [22]

Joint analysis of cluster number counts and weak lensing power spectrum to correct for the super-sample covariance

M. Takada and D.N. Spergel,Joint analysis of cluster number counts and weak lensing power spectrum to correct for the super-sample covariance,Monthly Notices of the Royal Astronomical Society441(2014) 2456 [1307.4399]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[23] [23]

Combining cluster number counts and galaxy clustering

F. Lacasa and R. Rosenfeld,Combining cluster number counts and galaxy clustering,Journal of Cosmology and Astroparticle Physics2016(2016) 005 [1603.00918]

work page internal anchor Pith review Pith/arXiv arXiv 2016

[24] [24]

Fast and easy super-sample covariance of large scale structure observables

F. Lacasa and J. Grain,Fast and easy super-sample covariance of large scale structure observables, Astronomy & Astrophysics624(2019) A61 [1809.05437]

work page internal anchor Pith review Pith/arXiv arXiv 2019

[25] [25]

Gouyou Beauchamps, F

S. Gouyou Beauchamps, F. Lacasa, I. Tutusaus, M. Aubert, P. Baratta, A. Gorce et al.,Impact of survey geometry and super-sample covariance on future photometric galaxy surveys,Astronomy & Astrophysics659 (2022) A128 [2109.02308]

work page arXiv 2022

[26] [26]

Super-sample covariance approximations and partial sky coverage

F. Lacasa, M. Lima and M. Aguena,Super-sample covariance approximations and partial sky coverage, Astronomy & Astrophysics611(2018) A83 [1612.05958]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[27] [27]

Payerne, C

C. Payerne, C. Murray, C. Combet, C. Doux, A. Fumagalli and M. Penna-Lima,Testing the accuracy of likelihoods for cluster abundance cosmology,Monthly Notices of the Royal Astronomical Society520(2023) 6223 [2210.11093]

work page arXiv 2023

[28] [28]

Payerne, C

C. Payerne, C. Murray, C. Combet and M. Penna-Lima,Towards including super-sample covariance in the unbinned likelihood for cluster abundance cosmology,Monthly Notices of the Royal Astronomical Society (2024) stae1504 [2401.10024]

work page arXiv 2024

[29] [29]

Fumagalli, A

A. Fumagalli, A. Saro, S. Borgani, T. Castro, M. Costanzi, P. Monaco et al.,Euclid : Effects of sample covariance on the number counts of galaxy clusters,Astronomy & Astrophysics652(2021) A21 [2102.08914]

work page arXiv 2021

[30] [30]

eROSITA cluster cosmology forecasts: cluster temperature substructure bias

F. Hofmann, J. Sanders, N. Clerc, K. Nandra, J. Ridl, K. Dennerl et al.,erosita cluster cosmology forecasts: Cluster temperature substructure bias,Astronomy & Astrophysics606(2017) A118 [1708.05205]. – 32 –

work page internal anchor Pith review Pith/arXiv arXiv 2017

[31] [31]

Lacasa, M

F. Lacasa, M. Aubert, P. Baratta, J. Carron, A. Gorce, S.G. Beauchamps et al.,Efficient computation of the super-sample covariance for stage iv galaxy surveys,Astronomy & Astrophysics671(2023) A115 [2209.14421]

work page arXiv 2023

[32] [32]

Ishida, S.D.P

E.E.O. Ishida, S.D.P. Vitenti, M. Penna-Lima, J. Cisewski, R.S. de Souza, A.M.M. Trindade et al., COSMOABC: Likelihood-free inference via Population Monte Carlo Approximate Bayesian Computation, Astron. Comput.13(2015) 1 [1504.06129]

work page arXiv 2015

[33] [33]

Í.Zubeldia,B.Bolliet,A.ChallinorandW.Handley,Extractingcosmologicalinformationfromtheabundance of galaxy clusters with simulation-based inference,Physical Review D112(2025) 083536 [2504.10230]

work page arXiv 2025

[34] [34]

Cerardi, M

N. Cerardi, M. Pierre, F. Lanusse and X. Corap,The Cosmological analysis of X-ray cluster surveys: VII. Bypassing scaling relations with Lagrangian Deep Learning and Simulation-based inference,Astronomy & Astrophysics701(2025) A110 [2507.01820]

work page arXiv 2025

[35] [35]

Ntampaka, A

M. Ntampaka, A. Ciprijanovic, A.M. Delgado, J. Soltis, J.F. Wu, M. Yunus et al.,The Importance of Being Adaptable: An Exploration of the Power and Limitations of Domain Adaptation for Simulation-Based Inference with Galaxy Clusters,arXiv e-prints(2025) arXiv:2510.09748 [2510.09748]

work page arXiv 2025

[36] [36]

Simulation-based cosmological inference from optically-selected galaxy clusters with $\texttt{Capish}$

C. Payerne, C. Murray and H. Simon,Simulation-based cosmological inference from optically-selected galaxy clusters withCapish,arXiv e-prints(2026) arXiv:2602.01911 [2602.01911]

work page internal anchor Pith review Pith/arXiv arXiv 2026

[37] [37]

J. Prat, J. Zuntz, C. Chang, T. Tröster, E. Pedersen, C. García-García et al.,The catalog-to-cosmology framework for weak lensing and galaxy clustering for lsst,The Open Journal of Astrophysics6(2023) [2212.09345]

work page arXiv 2023

[38] [38]

Fumagalli, M

A. Fumagalli, M. Costanzi, A. Saro, T. Castro and S. Borgani,Cosmological constraints from the abundance, weak lensing, and clustering of galaxy clusters: Application to the SDSS,Astronomy & Astrophysics682 (2024) A148 [2310.09146]

work page arXiv 2024

[39] [39]

Galaxy-galaxy weak lensing in SDSS: intrinsic alignments and shear calibration errors

C.M. Hirata, R. Mandelbaum, U. Seljak, J. Guzik, N. Padmanabhan, C. Blake et al.,Galaxy-galaxy weak lensing in the Sloan Digital Sky Survey: intrinsic alignments and shear calibration errors,Monthly Notices of the Royal Astronomical Society353(2004) 529 [astro-ph/0403255]

work page internal anchor Pith review Pith/arXiv arXiv 2004

[40] [40]

Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix

J. Hartlap, P. Simon and P. Schneider,Why your model parameter confidences might be too optimistic. unbiased estimation of the inverse covariance matrix,Astronomy & Astrophysics464(2006) 399–404 [astro-ph/0608064]

work page internal anchor Pith review Pith/arXiv arXiv 2006

[41] [41]

Dependence of cosmic shear covariances on cosmology - Impact on parameter estimation

T. Eifler, P. Schneider and J. Hartlap,Dependence of cosmic shear covariances on cosmology-impact on parameter estimation,Astronomy & Astrophysics502(2009) 721 [0810.4254]

work page internal anchor Pith review Pith/arXiv arXiv 2009

[42] [42]

Cosmological parameter constraints from galaxy-galaxy lensing and galaxy clustering with the SDSS DR7

R. Mandelbaum, A. Slosar, T. Baldauf, U. Seljak, C.M. Hirata, R. Nakajima et al.,Cosmological parameter constraints from galaxy-galaxy lensing and galaxy clustering with the SDSS DR7,Monthly Notices of the Royal Astronomical Society432(2013) 1544 [1207.1120]

work page internal anchor Pith review Pith/arXiv arXiv 2013

[43] [43]

CosmoLike - Cosmological Likelihood Analyses for Photometric Galaxy Surveys

E. Krause and T. Eifler,cosmolike – cosmological likelihood analyses for photometric galaxy surveys,Monthly Notices of the Royal Astronomical Society470(2017) 2100 [1601.05779]

work page internal anchor Pith review Pith/arXiv arXiv 2017

[44] [44]

Precision matrix expansion - efficient use of numerical simulations in estimating errors on cosmological parameters

O. Friedrich and T. Eifler,Precision matrix expansion - efficient use of numerical simulations in estimating errors on cosmological parameters,Monthly Notices of the Royal Astronomical Society473(2018) 4150 [1703.07786]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[45] [45]

The Effect of Covariance Estimator Error on Cosmological Parameter Constraints

S. Dodelson and M.D. Schneider,The effect of covariance estimator error on cosmological parameter constraints,Physical Review D88(2013) [1304.2593]

work page internal anchor Pith review Pith/arXiv arXiv 2013

[46] [46]

Biases on cosmological parameter estimators from galaxy cluster number counts

M. Penna-Lima, M. Makler and C.A. Wuensche,Biases on cosmological parameter estimators from galaxy cluster number counts,Journal of Cosmology and Astroparticle Physics2014(2014) 039 [1312.4430]

work page internal anchor Pith review Pith/arXiv arXiv 2014

[47] [47]

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

E. Abdalla, G.F. Abellán, A. Aboubrahim, A. Agnello, Ö. Akarsu, Y. Akrami et al.,Cosmology intertwined: A review of the particle physics, astrophysics, and cosmology associated with the cosmological tensions and anomalies,Journal of High Energy Astrophysics34(2022) 49 [2203.06142]. – 33 –

work page internal anchor Pith review Pith/arXiv arXiv 2022

[48] [48]

Pantos and L

I. Pantos and L. Perivolaropoulos,Status of the𝑆8 Tension: A 2026 Review of Probe Discrepancies,arXiv e-prints(2026) arXiv:2602.12238 [2602.12238]. [49]Planckcollaboration,Planck 2018 results. VI. Cosmological parameters,Astron. Astrophys.641(2020) A6 [1807.06209]

work page arXiv 2026

[49] [49]

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,Astronomy & Astrophysics645(2021) A104 [2007.15633]

work page arXiv 2021

[50] [50]

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,Physical Review D108(2023) 123519

2023

[51] [51]

Sunayama, H

T. Sunayama, H. Miyatake, S. Sugiyama, S. More, X. Li, R. Dalal et al.,Optical cluster cosmology with SDSS redMaPPer clusters and HSC-Y3 lensing measurements,Physical Review D110(2024) 083511 [2309.13025]

work page arXiv 2024

[52] [52]

Miyatake,Cosmology with Galaxy Clusters,arXiv e-prints(2025) arXiv:2505.07697 [2505.07697]

H. Miyatake,Cosmology with Galaxy Clusters,arXiv e-prints(2025) arXiv:2505.07697 [2505.07697]

work page arXiv 2025

[53] [53]

NumCosmo: Numerical Cosmology

S. Dias Pinto Vitenti and M. Penna-Lima, “NumCosmo: Numerical Cosmology.” Astrophysics Source Code Library ascl:1408.013, Aug., 2014

2014

[54] [54]

J.Tinker, A.V.Kravtsov, A.Klypin, K.Abazajian, M.Warren, G.Yepesetal.,Towardahalomassfunctionfor precision cosmology: The limits of universality,The Astrophysical Journal688(2008) 709 [0803.2706]

work page internal anchor Pith review Pith/arXiv arXiv 2008

[55] [55]

The universality of the virial halo mass function and models for non-universality of other halo definitions

G. Despali, C. Giocoli, R.E. Angulo, G. Tormen, R.K. Sheth, G. Baso et al.,The universality of the virial halo mass function and models for non-universality of other halo definitions,Monthly Notices of the Royal Astronomical Society456(2016) 2486 [1507.05627]

work page internal anchor Pith review Pith/arXiv arXiv 2016

[56] [56]

Semi-analytic predictions for statistical properties of X-ray clusters of galaxies in cold dark matter universes

T. Kitayama and Y. Suto,Semi-analytic predictions for statistical properties of x-ray clusters of galaxies in cold dark matter universes,The Astrophysical Journal469(1996) 480 [astro-ph/9604141]

work page internal anchor Pith review Pith/arXiv arXiv 1996

[57] [57]

Baryonic Features in the Matter Transfer Function

D.J. Eisenstein and W. Hu,Baryonic features in the matter transfer function,The Astrophysical Journal496 (1998) 605 [astro-ph/9709112]

work page internal anchor Pith review Pith/arXiv arXiv 1998

[58] [58]

Kaiser,On the spatial correlations of Abell clusters., vol

N. Kaiser,On the spatial correlations of Abell clusters., vol. 284 (1984), 10.1086/184341

work page doi:10.1086/184341 1984

[59] [59]

An analytic model for the spatial clustering of dark matter haloes

H. Mo and S.D. White,An analytic model for the spatial clustering of dark matter haloes,Monthly Notices of the Royal Astronomical Society282(1996) 347 [astro-ph/9512127]

work page internal anchor Pith review Pith/arXiv arXiv 1996

[60] [60]

The Large Scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests

J.L. Tinker, B.E. Robertson, A.V. Kravtsov, A. Klypin, M.S. Warren, G. Yepes et al.,The large-scale bias of dark matter halos: Numerical calibration and model tests,The Astrophysical Journal724(2010) 878 [1001.3162]

work page internal anchor Pith review Pith/arXiv arXiv 2010

[61] [61]

Ishiyama et al.,The Uchuu simulations: Data Release 1 and dark matter halo concentrations,Monthly Notices of the Royal Astronomical Society506(2021) 4210 [2007.14720]

T. Ishiyama et al.,The Uchuu simulations: Data Release 1 and dark matter halo concentrations,Monthly Notices of the Royal Astronomical Society506(2021) 4210 [2007.14720]

work page arXiv 2021

[62] [62]

Constraints on the mass-richness relation from the abundance and weak lensing of SDSS clusters

R. Murata, T. Nishimichi, M. Takada, H. Miyatake, M. Shirasaki, S. More et al.,Constraints on the mass–richness relation from the abundance and weak lensing of sdss clusters,The Astrophysical Journal854 (2018) 120 [1707.01907]

work page internal anchor Pith review Pith/arXiv arXiv 2018

[63] [63]

Mandelbaum, T

R. Mandelbaum, T. Eifler, R. Hložek, T. Collett, E. Gawiser, D. Scolnic et al.,The lsst dark energy science collaboration(desc)sciencerequirementsdocument,arXivpreprintarXiv:1809.01669(2018) [1809.01669]

work page arXiv 2018

[64] [64]

D P Vitenti and E.J

S. D P Vitenti and E.J. Barroso,Apes: approximate posterior ensemble sampler,Monthly Notices of the Royal Astronomical Society525(2023) 73 [2303.13667]. – 34 –

work page arXiv 2023