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Planck clusters calibrated with DES shear put S8 at 0.791, in 1.6-sigma tension with CMB and 2.9-sigma with eROSITA.

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Planck cluster counts with DES weak-lensing and Chandra mass calibration yield S8=0.791, matching late-time probes and disagreeing with eROSITA clusters by 2.9 sigma.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Careful PSZ2+DES shear S8=0.79 measurement, but the scatter-free hydrostatic-bias assumption is untested and the AIC-preferred free-bias model shifts Omega_m by 0.04. the 4 major comments →

arxiv 2509.02068 v1 pith:GRBTRE7W submitted 2025-09-02 astro-ph.CO

Cosmological constraints from the Planck cluster catalogue with DES shear profiles and Chandra observations

G. Aymerich , S. Grandis , M. Douspis , G. W. Pratt , L. Salvati , F. Andrade-Santos , S. Bocquet , M. Costanzi
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W. R. Forman C. Jones M. Aguena F. Andrade-Oliveira D. Bacon D. Brooks D. L. Burke J. Carretero L. N. da Costa M. E. da Silva Pereira T. M. Davis J. De Vicente S. Desai H. T. Diehl P. Doel S. Everett B. Flaugher J. Frieman E. Gaztanaga D. Gruen G. Gutierrez S. R. Hinton D. L. Hollowood K. Honscheid D. J. James S. Lee J. L. Marshall J. Mena-Fern\'andez R. Miquel J. J. Mohr R. L. C. Ogando A. A. Plazas Malag\'on A. Porredon J. Prat A. K. Romer S. Samuroff E. Sanchez D. Sanchez Cid M. Smith E. Suchyta M. E. C. Swanson D. L. Tucker N. Weaverdyck J. Weller M. Yamamoto
This is my paper
classification astro-ph.CO
keywords galaxy clustersSunyaev-Zeldovich effectweak gravitational lensingmass calibrationhydrostatic mass biasS8 tensioncosmological parametersPSZ2 catalogue
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.

The reading

The paper asks whether the low S8 value preferred by most late-time cosmological probes survives when the Planck cluster catalogue is mass-calibrated with wide-field weak-lensing shear rather than pointed follow-up observations. The authors jointly fit the PSZ2 cluster number counts and a hydrostatic mass bias calibrated on DES shear profiles, using Chandra X-ray observations to anchor the SZ-mass scaling relation, and find S8 = 0.791 (+0.023/-0.021), Omega_m = 0.312 (+0.018/-0.024), and a mean hydrostatic mass bias (1-b) = 0.844 (+0.055/-0.062). The result is in 1.6-sigma tension with Planck CMB constraints and in 2.9-sigma tension with the eROSITA cluster cosmology, even though the two analyses share the same DES mass-calibration procedure; direct mass comparison shows Planck+DES and eRASS1 masses agree, so the paper locates the disagreement in cluster population modelling, not mass calibration. If the claim holds, Planck clusters join the late-time low-S8 consensus, and the same joint-calibration machinery becomes a template for checking consistency between ICM-selected cluster samples.

Core claim

One joint likelihood — cluster number counts, DES shear-calibrated hydrostatic mass bias, and BAO data — turns the Planck PSZ2 catalogue into a competitive late-time cosmological probe. Baseline: Omega_m=0.312(+0.018,-0.024), sigma8=0.777(+/-0.024), S8=0.791(+0.023,-0.021), (1-b)=0.844(+0.055,-0.062). Letting the bias evolve with mass moves the preferred values to Omega_m=0.353, sigma8=0.751, S8=0.814, with alpha=0.272±0.094 preferred by the AIC. Results stay coherent across centre definitions, source-redshift estimators, and inner-bin choices. Planck and eROSITA masses agree, so the 2.9-sigma tension with eROSITA is placed in population modelling, not mass calibration.

What carries the argument

The load-bearing object is the hydrostatic mass bias (1-b), the factor that converts Chandra-derived hydrostatic masses to true halo masses through the scatter-free relation P(M_H|M,z)=delta(M_H-(1-b)M). The same bias enters both halves of the analysis: it rescales the masses that the DES shear-profile likelihood compares with a weak-lensing mass MWL, and it sets the expected SZ signal in the number-counts prediction. The argument is carried by the joint likelihood lnL = lnL_WL + lnL_NC + lnL_BAO, sampled with MCMC; the WL mass-to-halo-mass relation and its scatter are calibrated from synthetic shear profiles drawn from hydrodynamic simulations so that an imperfect extraction model does not

Load-bearing premise

The load-bearing premise is that a cluster's hydrostatic mass is the true halo mass times one smooth factor (1-b) with no scatter, so a single number or a single mass/redshift trend fully corrects the mass scale; the paper's own test that frees the mass trend shifts Omega_m from 0.312 to 0.353 and S8 from 0.791 to 0.814, showing this assumption's scope is the most fragile point.

What would settle it

Compare Chandra hydrostatic masses with unbiased lensing masses for the same PSZ2 clusters in narrow mass and redshift bins, with mis-centring controlled by X-ray centres. If the residuals show scatter clearly above zero around the (1-b) relation, or a mass trend steeper than alpha=0.27±0.09 outside the fitted uncertainty, then the delta-function mass-bias model in Eq. 9 is wrong and the quoted S8=0.791 is not the unbiased value. A cheaper check: rerun the joint fit with (1-b) given an intrinsic mass-scatter parameter and see whether the posterior on Omega_m moves by more than the reported err

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

If this is right

  • Planck PSZ2 number counts mass-calibrated with DES shear prefer S8=0.791, consistent with SPT SZ clusters and most late-time probes, and only 1.6-sigma below Planck CMB.
  • The mean hydrostatic mass bias (1-b)=0.844 agrees with simulation-based and gas-fraction-based estimates, supporting wide-field WL as a cluster mass calibrator.
  • Because Planck+DES and eRASS1 masses agree for matched clusters, the 2.9-sigma eROSITA tension is placed in selection-function/population modelling rather than in the shared mass calibration.
  • Letting the bias evolve with mass yields Omega_m=0.353 and S8=0.814, with the AIC preferring the evolving model; the fixed-bias baseline therefore carries a modelling choice that visibly moves the result along the Omega_m-sigma8 degeneracy.
  • Forecast with Stage IV lensing-like shear mocks shows the PSZ2 sample becomes nearly statistics-limited, with further gains requiring the WL bias uncertainty to drop from 2-4% toward 1%.

Where Pith is reading between the lines

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

  • Editorial extension: the same joint-calibration machinery, applied without modification to eROSITA and SPT catalogues, would directly test whether their differing S8 values are fully explained by catalogue population models.
  • Editorial extension: if the mass-dependent bias (alpha~0.27) is a real astrophysical feature rather than a degeneracy with the PSZ2 mass-redshift correlation, fixed-bias cluster analyses systematically underestimate Omega_m; an independent, scatter-free measurement of (1-b) in fine mass bins would arbitrate.
  • Editorial extension: the method transfers to X-ray-selected cluster samples — replacing the SZ selection function with an X-ray one while keeping the DES shear bias likelihood would place eROSITA and Planck on exactly the same calibration footing, a testable route to isolate selection effects.
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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

4 major / 5 minor

Summary. The paper presents cosmological constraints from the Planck PSZ2 cluster catalogue by simultaneously fitting (i) the cluster number counts, (ii) a weak-lensing calibration of the hydrostatic mass bias using DES Y3 shear profiles around 93 PSZ2 clusters, and (iii) BAO data. Hydrostatic masses for the full PSZ2 sample are derived from a YSZ–MH scaling relation calibrated on Chandra X-ray observations. The baseline analysis, using BCG centres, bpz photo-zs, and a fixed hydrostatic mass bias, yields Ωm=0.312+0.018/−0.024, σ8=0.777±0.024, S8=0.791+0.023/−0.021, and (1−b)=0.844+0.055/−0.062, in mild tension with Planck CMB and in 2.9σ tension with eRASS1. Robustness to centre definition, photo-z choice, inner-bin inclusion, and bias evolution is explored, and a forecast for Stage-IV WL surveys is given.

Significance. If the baseline result is correct, it adds a well-characterized late-time cluster probe to the low-S8 consensus and locates the eROSITA discrepancy in population modelling rather than mass calibration. The paper's method—simultaneous WL-based bias calibration and cosmological sampling—is a useful template for cluster cosmology with Stage-IV surveys. The analysis also provides a careful comparison of mass estimates with eRASS1 and makes chains publicly available. However, the central result depends on several modelling choices whose impact is not fully stress-tested, and the data themselves prefer an alternative parametrization, so the headline numbers should be treated with caution until those tests are performed.

major comments (4)
  1. [Eq. (9) and Sec. 4.1] Equation (9) assumes a scatter-free, deterministic hydrostatic mass bias, P(MH|M,z)=δ(MH−(1−b)M). This is what reduces Eq. (8) to Eq. (10) and allows the WL likelihood to be evaluated at M=MH/(1−b). If the hydrostatic mass has intrinsic scatter around (1−b)M (simulations and X-ray studies suggest several to ~15%), Eq. (10) is not the correct marginal likelihood; the integral over M must be retained, and the calibration of (1−b) and the number-counts likelihood will be modified. The robustness tests in Table 4 vary only the mean of the bias (α, β) and keep the delta-function form, so they do not probe this assumption. Given that freeing α already shifts Ωm from 0.312 to 0.353 and S8 from 0.791 to 0.814 (Table 4) and is AIC-preferred (Table 6), the no-scatter assumption is load-bearing and needs an explicit test, e.g., a rerun with a log-normal scatter in MH at fixed M.
  2. [Table 6 and Sec. 7.2] The paper reports ΔAIC=7.36 for the α-free model relative to the baseline fixed-bias model, which by the paper's own criterion is a significant improvement, yet the abstract, conclusions, and headline comparisons quote only the fixed-bias results. Since the data prefer the evolving-bias model, the fixed-bias model should not be presented as the sole baseline without a physical justification or a clear statement that the headline constraints are conditional on a prior that the data disfavour. The shifts between the two models are at the ~1σ level in S8 but larger in Ωm, so the choice affects the paper's central comparison with eRASS1 and Planck.
  3. [Sec. 7.2, Table 5] The number-counts C-statistic is 46.4 against an expected 34.5±7.9 from the best-fit model, i.e., about 1.5σ high. The paper attributes this to a known PSZ2 redshift-distribution problem and leaves it unmodelled. Because the number-counts likelihood is one of only two main likelihood terms, a systematic misfit of this size can bias the recovered Ωm and σ8. The paper should quantify the impact, for example by removing or down-weighting the discrepant redshift bins, or by adding a nuisance parameter for the redshift distribution, and show that the cosmological conclusions are stable.
  4. [Sec. 7.2, Fig. 6 and Table 5] The stacked shear profiles are visibly flatter than the model predictions (residuals in bins 2 and 3), and the baseline χ2=26.0+2.1/−2.7 for 17 dof is high. The paper argues this is absorbed by the WL mass bias bWL, but this is only guaranteed if the mismatch is scale-independent or if the simulation-based calibration covers the same radial trend. A mass-dependent residual trend could bias bM in Eq. (25) and hence the mass calibration. At minimum, the authors should test the sensitivity to the fixed concentration c500c=3 and show that the recovered masses are unchanged when the radial weighting is varied.
minor comments (5)
  1. [Abstract and Table 4] The abstract quotes the fixed-bias baseline without noting that the AIC-favoured model yields different Ωm and S8; consider making the baseline choice explicit in the abstract.
  2. [Sec. 3.3, Eq. (5)] The YSZ–MH scaling relation parameters are quoted with asymmetric notation (10−0.29±0.01 in Eq. 5 vs Y∗ in Eq. 3); clarify the relation between Y∗ and the normalization in Eq. (5).
  3. [Table 2 and Sec. 6.2] The notation 'BCG 800 bpzαβ' is compact but somewhat opaque; a short glossary or explicit definition in the table caption would improve readability.
  4. [Sec. 7.3, Fig. 10] The mass comparison with eRASS1 is a useful consistency check, but the vertical error bars appear to omit scatter in the eRASS1 mass estimates; please state the error budget explicitly.
  5. [Appendix C] The no-BAO results are reported for the baseline only; reporting them for the α-free model as well would be helpful for comparison with eRASS1, which uses a tighter H0 prior.

Circularity Check

1 steps flagged

Central S8 derivation is a genuine joint fit; only a minor shared-calibration cross-check is partially built in.

specific steps
  1. other [Section 7.3 (Comparison with other cosmological analyses), Eq. (39), Fig. 10]
    "We confirm that our mass calibration is consistent with the eROSITA analysis by comparing masses for clusters present in both Planck and eROSITA samples, eliminating it as a potential cause of tension. ... This might be expected, as both experiments use the same WL data, and treat it in very similar ways."

    The comparison mass MPlanck+DES is defined as MH/(1-b) (Eq. 39), with (1-b) calibrated from DES WL shear profiles; the eRASS1 masses are taken from Ghirardini+24, whose mass calibration uses the same DES WL data and the same Grandis+24 WL mass-to-halo-mass calibration. The agreement between the two mass scales is therefore partly guaranteed by the common WL calibration, so the 'confirmation' of mass-calibration consistency is not an independent validation. It does still test consistency between the SZ+X-ray and X-ray count-rate proxies, so this is a minor, non-load-bearing circularity; the central S8 constraint does not reduce to this comparison.

full rationale

The paper's headline result, S8 = 0.791, comes from a simultaneous fit of the PSZ2 number-count likelihood (Eqs. 26-29) and the DES shear-profile likelihood (Eqs. 8-11), with the hydrostatic-mass bias (1-b) and cosmology sampled together. The YSZ-MH scaling relation (Eq. 5) and its priors are imported from Aymerich+24, and the WL mass-to-halo-mass calibration (Eqs. 24-25, Appendix B) is imported from the Grandis+24 simulation framework. These are external inputs calibrated on X-ray, SZ, and simulation data, not on the target S8; they are load-bearing but not circular in the sense of being defined in terms of the result. The delta-function no-scatter assumption in Eq. (9) is an explicit modelling choice (justified by external references), not a hidden reduction. The paper's own AIC analysis shows that freeing the mass trend alpha is preferred, but this is a robustness concern rather than a circularity. The only partially circular element is the eRASS1 mass comparison, where both mass scales share the same DES WL calibration; the paper acknowledges this, and the comparison is a consistency check rather than part of the cosmological derivation. Overall, the central S8 value is not fixed by construction or by a self-citation chain, so the circularity score is low.

Axiom & Free-Parameter Ledger

7 free parameters · 8 axioms · 0 invented entities

The central S8 constraint rests on a long chain of upstream assumptions: hydrostatic equilibrium, a scatter-free mass bias, the Tinker mass function, a Gaussian-noise selection function, simulation-calibrated WL bias, fixed NFW concentration, and self-similar scaling. Only the cosmological parameters and (1-b) are free at the level of this paper; everything else is adopted from prior literature, mostly the authors' own previous work (Aymerich+24, Grandis+24).

free parameters (7)
  • Hydrostatic mass bias (1-b) = 0.844+0.055-0.062 (baseline)
    Mean correction from X-ray hydrostatic masses to true halo masses, constrained jointly by DES shear profiles and PSZ2 number counts.
  • Bias mass trend alpha and redshift trend beta = alpha=0.272+/-0.094, beta=0.12+0.22-0.19 when free
    Evolution parameters of (1-b) in eq. 12; freeing alpha shifts Omega_m by about 0.04 and is preferred by AIC.
  • YSZ-MH scaling relation parameters Y*, alpha_SZ, sigma_int = Y*=-0.29+/-0.01, alpha_SZ=1.70+/-0.1, sigma_int=0.086+/-0.01
    Gaussian priors from Aymerich+24 (shared author set) calibrated on the Chandra ESZ sample; they set the hydrostatic masses used in both likelihoods.
  • WL systematic parameters A_WL, B_WL, C_WL, D_WL = Standard Gaussian priors
    Marginalize over simulation-derived uncertainties of the WL mass-to-halo mass relation (Appendix B).
  • Mis-centring parameters sigma1, sigma2, f = SZ sigma1=54.9+/-5.4 arcsec; BCG sigma1=21+/-2 kpc, sigma2=207+/-39 kpc, f=0.54+/-0.19
    Fitted on 29 clusters with Chandra reference centres; enter the shear extraction model through R_extr_mis (eq. 20).
  • NFW concentration c500c = 3 (fixed)
    Hand-fixed concentration in the shear extraction model; the paper argues any bias from this choice is absorbed by the simulation-calibrated WL bias.
  • WL mass bias, mass trend, and scatter (b(z), b_M, sigma_WL) = mu_b approx -0.01 to -0.03, b_M approx 1.0, sigma_WL approx 0.2 (Tables B.1-B.5)
    Calibrated from TNG300 simulations within the Grandis+24 framework; they define the mapping from WL mass to halo mass.
axioms (8)
  • domain assumption Hydrostatic equilibrium for X-ray mass computation
    Section 3.1: gas density and temperature profiles from Chandra are converted to total mass assuming pressure support balances gravity.
  • domain assumption Scatter-free hydrostatic mass-halo mass relation (eq. 9)
    Section 4.1: P(MH|M,z)=delta(MH-(1-b)M), following Planck XX/XXIV; no intrinsic scatter in the X-ray mass proxy.
  • domain assumption Tinker et al. (2008) halo mass function
    Section 5.1: the theoretical cluster abundance is computed with this mass function; a different mass function shifts the predicted counts.
  • domain assumption Gaussian-noise analytical selection function
    Section 5.1: survey selection approximated from Planck XXIV (2016) assuming pure Gaussian noise, giving an error-function form for P[q|qbar_m].
  • domain assumption Mis-centring shapes: single and double Rayleigh distributions
    Section 2.4, eqs. 1-2: SZ mis-centring follows a Rayleigh in angle, optical mis-centring a two-Rayleigh mixture in physical distance; fitted on only 29 clusters.
  • domain assumption Log-normal WL mass-halo mass relation with TNG300-calibrated mean and scatter
    Section 4.2.3, eqs. 24-25: the WL mass bias and scatter are taken from hydrodynamic simulations of the authors' own pipeline.
  • domain assumption DES calibration sample represents the full PSZ2 sample
    Section 2.3: the 93 clusters in the DES footprint are assumed representative because only sky position selects them; a mass or redshift-dependent footprint effect would bias the calibration.
  • domain assumption Self-similar redshift scaling of the YSZ-MH relation
    Eq. 3: E^{-2/3}(z) DA^2 YSZ scaling is assumed, extrapolating the z<0.35 Chandra calibration to the full sample out to z~1.

reviewed 2026-08-05 · how reviews work

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Cite this review

Pith. "Pith review of Cosmological constraints from the Planck cluster catalogue with DES shear profiles and Chandra observations." pith.science (2026). https://pith.science/paper/GRBTRE7W

@misc{pith2026250902068,
  author       = {Pith},
  title        = {Pith review of: Cosmological constraints from the Planck cluster catalogue with DES shear profiles and Chandra observations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GRBTRE7W}},
  note         = {Machine review of arXiv:2509.02068}
}
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abstract

We present cosmological constraints from the Planck PSZ2 cosmological cluster sample, using weak-lensing shear profiles from Dark Energy Survey (DES) data and X-ray observations from the Chandra telescope for the mass calibration. We compute hydrostatic mass estimates for all clusters in the PSZ2 sample with a scaling relation between their Sunyaev-Zeldovich signal and X-ray derived hydrostatic mass, calibrated with the Chandra data. We introduce a method to correct these masses with a hydrostatic mass bias using shear profiles from wide-field galaxy surveys. We simultaneously fit the number counts of the PSZ2 sample and the mass calibration with the DES data, finding $\Omega_\text{m}=0.312^{+0.018}_{-0.024}$, $\sigma_8=0.777\pm 0.024$, $S_8\equiv \sigma_8 \sqrt{\Omega_\text{m} / 0.3}=0.791^{+0.023}_{-0.021}$, and $(1-b)=0.844^{+0.055}_{-0.062}$ for our baseline analysis when combined with BAO data. When considering a hydrostatic mass bias evolving with mass, we find $\Omega_\text{m}=0.353^{+0.025}_{-0.031}$, $\sigma_8=0.751\pm 0.023$, and $S_8=0.814^{+0.019}_{-0.020}$. We verify the robustness of our results by exploring a variety of analysis settings, with a particular focus on the definition of the halo centre used for the extraction of shear profiles. We compare our results with a number of other analyses, in particular two recent analyses of cluster samples obtained from SPT and eROSITA data that share the same mass calibration data set. We find that our results are in overall agreement with most late-time probes, in very mild tension with CMB results (1.6$\sigma$), and in significant tension with results from eROSITA clusters (2.9$\sigma$). We confirm that our mass calibration is consistent with the eROSITA analysis by comparing masses for clusters present in both Planck and eROSITA samples, eliminating it as a potential cause of tension.

Figures

Figures reproduced from arXiv: 2509.02068 by A. A. Plazas Malag\'on, A. K. Romer, A. Porredon, B. Flaugher, C. Jones, D. Bacon, D. Brooks, D. Gruen, D. J. James, D. L. Burke, D. L. Hollowood, D. L. Tucker, D. Sanchez Cid, E. Gaztanaga, E. Sanchez, E. Suchyta, F. Andrade-Oliveira, F. Andrade-Santos, G. Aymerich, G. Gutierrez, G. W. Pratt, H. T. Diehl, J. Carretero, J. De Vicente, J. Frieman, J. J. Mohr, J. L. Marshall, J. Mena-Fern\'andez, J. Prat, J. Weller, K. Honscheid, L. N. da Costa, L. Salvati, M. Aguena, M. Costanzi, M. Douspis, M. E. C. Swanson, M. E. da Silva Pereira, M. Smith, M. Yamamoto, N. Weaverdyck, P. Doel, R. L. C. Ogando, R. Miquel, S. Bocquet, S. Desai, S. Everett, S. Grandis, S. Lee, S. R. Hinton, S. Samuroff, T. M. Davis, W. R. Forman.

Figure 1
Figure 1. Figure 1: Mass and redshift distribution of the PSZ2 and DES calibration samples. The masses used for the plot are the hydrostatic masses derived in Sect. 3.4. Our analysis uses the same selection of lensing source galax￾ies in tomographic bins as the DES cosmic shear analysis (Amon et al. 2022; Secco et al. 2022). This selection is defined in Myles et al. (2021), which estimates the source redshifts with Self￾Organ… view at source ↗
Figure 2
Figure 2. Figure 2: Final cosmological constraints obtained for the BCG 800 bpz, BCG 500 bpz and BCG 800 dnf analysis settings and comparison with constraints from SZ number counts obtained in Aymerich et al. (2024) and constraints from CMB primary anisotropies from Planck Collabo￾ration VI (2020). 0.26 0.30 0.34 0.38 Ωm 0.6 0.7 0.8 0.9 1.0 (1 − b) 0.75 0.80 0.85 σ8 0.75 0.80 0.85 σ8 0.6 0.7 0.8 0.9 1.0 (1−b) BCG 800 bpz MCMF… view at source ↗
Figure 3
Figure 3. Figure 3: Final cosmological constraints obtained with the three different centre definitions used in this work (BCG, MCMF and SZ). coherence. No combination of analysis settings leads to results in significant tension with the baseline analysis. With the excep￾tion of the scenarios with a bias evolving with mass, the results are even in very good agreement, deviating from the baseline by 0.3 0.4 Ωm −0.5 0.0 0.5 β 0… view at source ↗
Figure 5
Figure 5. Figure 5: Comparison of the S 8 constraints (with 68% confidence inter￾vals) obtained with the different analysis settings combination. 7.2. Goodness of fit In this section, we evaluate the goodness of fit (GoF) of the var￾ious fits performed in the analysis. We do not present GoF re￾sults for the YSZ − MH scaling relation as they can be found in Aymerich et al. (2024), and focus on the GoF of the mass cal￾ibration … view at source ↗
Figure 6
Figure 6. Figure 6: Top row: Comparison of stacked tangential shear profile (data points) with the prediction from the best-fit model (lines), for the baseline analysis (left panel), MCMCF 800 bpz analysis (central panel), and SZ 800 bpz analysis (right panel). The shaded area corresponds to the inner bin, ignored in all analyses except BCG 500 bpz. Bottom row: Residuals rescaled by the uncertainty. The shaded area correspond… view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of the S 8 constraints (with 68% confidence inter￾vals) obtained in the baseline analysis of this work with other recent analyses. data. The fact that we obtain slightly tighter constraints than Bocquet et al. (2024b), despite having roughly half the num￾ber of clusters, can be explained by five reasons. First, while the sample is smaller, the constraining power of cluster studies is currently l… view at source ↗
Figure 10
Figure 10. Figure 10: For the eRASS1 mass, we directly take the mass and un￾certainty from the eRASS1 catalogue, computed using the best￾fit cosmology and scaling relations from Ghirardini et al. (2024). For the Planck+DES mass, we take the hydrostatic masses de￾rived in Sect. 3.4 and divide them by the best-fit bias of our base￾line analysis: MPlanck+DES = MH (1 − b) . (39) The vertical error bars in [PITH_FULL_IMAGE:figures… view at source ↗
Figure 11
Figure 11. Figure 11: Constraining power forecast for LSST-Rubin-like WL data, compared to the current baseline analysis with DES WL data, and no error on the mass bias. PSZ2 cluster sample can be greatly improved with Stage IV WL, it will be close to statistics limited, even though we assumed the same mis-centring distribution as the current analysis. We note that this can only be achieved if the uncertainty on the WL mass bi… view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 5, 2026.