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Multiprobe Cosmology from the Abundance of SPT Clusters and DES Galaxy Clustering and Weak Lensing

T0 review · 2 major / 3 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Combining South Pole Telescope cluster counts with DES galaxy clustering and weak lensing measures $\Omega_\mathrm{m}=0.300\pm0.017$ and $\sigma_8=0.797\pm0.026$, with $S_8=0.796\pm0.013$.

desk verdict A credible, well-documented SPT cluster + DES 3x2pt joint analysis with Planck-competitive constraints; the cross-covariance test is approximate but the result is believable. read the letter →

arxiv 2412.07765 v2 pith:XQ74TVMF submitted 2024-12-10 astro-ph.CO

S. Bocquet , S. Grandis , E. Krause , C. To , L. E. Bleem , M. Klein , J. J. Mohr , T. Schrabback
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A. Alarcon O. Alves A. Amon F. Andrade-Oliveira E. J. Baxter K. Bechtol M. R. Becker G. M. Bernstein J. Blazek H. Camacho A. Campos A. Carnero Rosell M. Carrasco Kind R. Cawthon C. Chang R. Chen A. Choi J. Cordero M. Crocce C. Davis J. DeRose H. T. Diehl S. Dodelson C. Doux A. Drlica-Wagner K. Eckert T. F. Eifler F. Elsner J. Elvin-Poole S. Everett X. Fang A. Ferté P. Fosalba O. Friedrich J. Frieman M. Gatti G. Giannini D. Gruen R. A. Gruendl I. Harrison W. G. Hartley K. Herner H. Huang E. M. Huff D. Huterer M. Jarvis N. Kuropatkin P.-F. Leget P. Lemos A. R. Liddle N. MacCrann J. McCullough J. Muir J. Myles A. Navarro-Alsina S. Pandey Y. Park A. Porredon J. Prat M. Raveri R. P. Rollins A. Roodman R. Rosenfeld E. S. Rykoff C. Sánchez J. Sanchez L. F. Secco I. Sevilla-Noarbe E. Sheldon T. Shin M. A. Troxel I. Tutusaus T. N. Varga N. Weaverdyck R. H. Wechsler H.-Y. Wu B. Yanny B. Yin Y. Zhang J. Zuntz T. M. C. Abbott P. A. R. Ade M. Aguena S. Allam S. W. Allen A. J. Anderson B. Ansarinejad J. E. Austermann M. Bayliss J. A. Beall A. N. Bender B. A. Benson F. Bianchini M. Brodwin D. Brooks L. Bryant D. L. Burke R. E. A. Canning J. E. Carlstrom J. Carretero F. J. Castander C. L. Chang P. Chaubal H. C. Chiang T-L. Chou R. Citron C. Corbett Moran M. Costanzi T. M. Crawford A. T. Crites L. N. da Costa M. E. S. Pereira T. M. Davis T. de Haan M. A. Dobbs P. Doel W. Everett A. Farahi B. Flaugher A. M. Flores B. Floyd J. Gallicchio E. Gaztanaga E. M. George M. D. Gladders N. Gupta G. Gutierrez N. W. Halverson S. R. Hinton J. Hlavacek-Larrondo G. P. Holder D. L. Hollowood W. L. Holzapfel J. D. Hrubes N. Huang J. Hubmayr K. D. Irwin D. J. James F. Kéruzoré G. Khullar K. Kim L. Knox R. Kraft K. Kuehn O. Lahav A. T. Lee S. Lee D. Li C. Lidman M. Lima A. Lowitz G. Mahler A. Mantz J. L. Marshall M. McDonald J. J. McMahon J. Mena-Fernández S. S. Meyer R. Miquel J. Montgomery T. Natoli J. P. Nibarger G. I. Noble V. Novosad R. L. C. Ogando S. Padin P. Paschos S. Patil A. A. Plazas Malagón C. Pryke C. L. Reichardt J. Roberson A. K. Romer C. Romero J. E. Ruhl B. R. Saliwanchik L. Salvati S. Samuroff E. Sanchez B. Santiago A. Sarkar A. Saro K. K. Schaffer K. Sharon C. Sievers G. Smecher M. Smith T. Somboonpanyakul M. Sommer B. Stalder A. A. Stark J. Stephen V. Strazzullo E. Suchyta M. E. C. Swanson G. Tarle D. Thomas C. Tucker D. L. Tucker T. Veach J. D. Vieira A. von der Linden G. Wang N. Whitehorn W. L. K. Wu V. Yefremenko M. Young J. A. Zebrowski H. Zohren DES Collaboration SPT Collaboration
This is my paper · ORCID
classification astro-ph.CO
keywords cosmologicalconstraintsgalaxyclustersSunyaev-Zeldovicheffectweaklensingclustering3x2ptclusterabundanceS8tension
verification ladder T0 review T1 audit T2 compute T3 formal

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 sets out to show that two late-Universe probes—the abundance of galaxy clusters detected by the South Pole Telescope, calibrated with weak-lensing masses, and the galaxy clustering plus weak-lensing (3×2pt) measurements of the Dark Energy Survey—can be combined into a single cosmological analysis without building a joint covariance pipeline. The authors demonstrate that the two datasets are statistically independent to a high degree, so the joint posterior follows from multiplying their likelihoods while tracking the one significant shared systematic. Marginalized over the remaining cosmological parameters and 52 nuisance parameters, the joint analysis measures $\Omega_\mathrm{m}=0.300\pm0.017$ and $\sigma_8=0.797\pm0.026$, which yields $S_8=0.796\pm0.013$—$1.6\sigma$ below the Planck CMB value. The same framework, combined with Planck, gives a 95% upper limit of $\sum m_\nu < 0.25\,\mathrm{eV}$ on the neutrino mass sum, and in $w$CDM returns $w=-1.15^{+0.23}_{-0.17}$ (or $-1.20^{+0.15}_{-0.09}$ with Planck). These results matter because they show that late-time large-scale-structure measurements have reached a precision rivaling early-universe CMB constraints, providing an independent check and a blueprint for future multiprobe surveys.

What carries the argument

The load-bearing machinery is the demonstration of statistical independence between the two data vectors, quantified by a halo-model cross-covariance calculation that shows the full covariance changes the combined signal-to-noise ratio by about 0.05% relative to shape and shot noise alone. That justifies adding the two log-likelihoods rather than constructing a joint covariance matrix. The combined posterior is then evaluated in the full 52-parameter space by training normalizing flows on each individual posterior and importance sampling one flow against the other; the implementation allows weighted samples. The only shared systematic that matters is the $\rho=-0.81$ correlation between the cluster weak-lensing mass bias and the photo-z bias of the fourth DES tomographic bin, which is imposed through a weight update during importance sampling.

What would settle it

A direct falsifier is to compute the full cross-covariance between the actual unbinned hierarchical cluster likelihood data vector and the 3×2pt data vector, including optical-richness cleaning and the true scale cuts, and compare the signal-to-noise ratio with and without the cross terms; if the difference exceeds roughly 0.05% (the paper's quoted value), the independence assumption and the resulting joint constraints would need revision.

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Extended reading notes

Core claim

The central claim is that the SPT cluster abundance and DES 3×2pt likelihoods can be combined almost exactly by simple addition. A halo-model calculation of the full covariance, including coupling of long-wavelength matter modes between the two probes, changes the combined signal-to-noise ratio by roughly 0.05%; the cluster data vector is dominated by shot noise and shape noise, and the 3×2pt data are insensitive to the small scales used in cluster mass calibration. The joint posterior is therefore built by importance sampling normalizing-flow representations of the two individual posteriors, with a single correlated systematic imposed between the cluster weak-lensing mass bias and the photo-z bias of the fourth tomographic bin ($\rho=-0.81$). Marginalized over all remaining parameters, the joint analysis recovers $\Omega_\mathrm{m}=0.300\pm0.017$, $\sigma_8=0.797\pm0.026$, and $S_8=0.796\pm0.013$.

Load-bearing premise

The load-bearing assumption is that the SPT cluster data and the DES 3×2pt data are statistically independent enough that their cross-covariance can be ignored; if the true cross-covariance is larger than the binned halo-model estimate, the quoted joint uncertainties will be underestimated.

Editorial extensions

If this is right

  • The joint SPT clusters + DES 3×2pt 95% credible region in the $\Omega_\mathrm{m}$–$\sigma_8$ plane is only 15% larger than the Planck 2018 primary CMB region, with a two-parameter probability-to-exceed of 0.22.
  • The combined SPT clusters + DES 3×2pt + Planck dataset breaks the $\sum m_\nu$–$\Omega_\mathrm{m}$ and $\sum m_\nu$–$\sigma_8$ degeneracies inherent in CMB-only data and gives a 95% upper limit $\sum m_\nu<0.25\,\mathrm{eV}$.
  • In $w$CDM, the joint dataset alone yields $w=-1.15^{+0.23}_{-0.17}$, and with Planck $w=-1.20^{+0.15}_{-0.09}$, a 1.7σ difference from a cosmological constant.
  • The area ratio of 95% credible regions for SPT clusters, DES 3×2pt, and the joint analysis is 3.3 : 2.1 : 1, showing that the combined probe is substantially tighter than either alone.
  • The recovered $S_8=0.796\pm0.013$ lies below the Planck value at the 1.6σ level, consistent with the low-$S_8$ tendency seen in other late-Universe analyses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extension: the independence of cluster and 3×2pt data vectors is likely to erode as cluster samples grow, so the same halo-model cross-covariance test should be rerun on simulated surveys before the sum-of-likelihoods shortcut is applied to next-generation data.
  • Extension: the same normalizing-flow importance-sampling architecture can be reused for any pair of probes that share a lensing source catalog; the key step is identifying principal shared systematics through Monte Carlo calibration, as done here for $\rho=-0.81$.
  • Extension: a direct test of the independence assumption would be to compute the cross-covariance with the actual unbinned hierarchical cluster likelihood and optical-richness cleaning, rather than the binned stacked approximation; the paper's own SNR difference of 0.05% is the target.
  • Extension: the $w$CDM shift toward $w<-1$ when Planck is included weakens to about 1σ if the CMB lensing amplitude $A_L$ is allowed to vary freely, so the 1.7σ result may be entangled with Planck's known excess lensing signal.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. This paper presents joint cosmological constraints from the SPT SZ-selected cluster abundance, with DES and HST weak-lensing mass calibration for 1,005 clusters, and the DES Y3 3x2pt galaxy clustering and cosmic shear measurements. The two previously published likelihoods are combined by summing their log-likelihoods under the assumption that their cosmological cross-covariance is negligible (Sec. III A), while a measured correlation rho = -0.81 between the cluster lensing mass-bias parameter b_WL and the DES photo-z bias Delta z^4_s is imposed through Eq. (5) (Sec. III B). Inference is performed by importance sampling between the two posteriors, represented by trained normalizing flows over an eight-dimensional subspace (Sec. III C). In flat Lambda CDM with massive neutrinos the joint analysis yields Omega_m = 0.300 +/- 0.017, sigma_8 = 0.797 +/- 0.026, and S_8 = 0.796 +/- 0.013 (1.6 sigma below Planck), with a 95% credible region only 15% larger than Planck's in the Omega_m-sigma_8 plane; with Planck it gives sum m_nu < 0.25 eV at 95%, and in wCDM it gives w = -1.15 (+0.23/-0.17) alone and w = -1.20 (+0.15/-0.09) with Planck.

Significance. These are the first joint SPT-cluster + DES 3x2pt constraints of this kind, and if they hold they demonstrate that a combined late-time probe can match Planck primary-CMB constraining power in the Omega_m-sigma_8 plane, an important benchmark for next-generation surveys. The methodology is careful and unusually well tested: both likelihoods are inherited from previously reviewed analyses; the independence assumption is stress-tested with an analytic halo-model SNR calculation; the importance-sampling pipeline is checked by reverse-direction IS and by flow-versus-chain comparisons (Fig. 6, Appendix B); the shared-lensing-systematics correlation is shown in Appendix A to be cosmologically negligible; and the flowjax-based analysis code is released. The headline numbers are falsifiable predictions (the 1.6 sigma S8 offset from Planck, the 1.7 sigma w deviation in wCDM, and the mild neutrino-mass preference), and the paper is candid about the limits of its approximations.

major comments (2)
  1. [Sec. III A] The negligibility of the cross-covariance between the SPT cluster likelihood and the DES 3x2pt likelihood is load-bearing for every headline number in Table I, because Eqs. (1) and (2) are simply summed. The supporting test is an SNR calculation [Eq. (4)] on a binned, stacked halo-model data vector that (i) ignores the optical richness cleaning used in the actual cluster selection, (ii) models the shape-noise cross-term only inside the halo-model framework rather than from the actual source-galaxy overlap, and (iii) is extrapolated to the unbinned hierarchical likelihood through a factor-of-six bin-count check. The reported 0.05% SNR change is reassuring, and in the covariance-dominated regime it is a reasonable proxy for parameter-level impact; the residual gap is that the paper never translates the SNR change into a bound on the shift of the Omega_m-sigma_8 posterior. I request either an explicit argument (e.g., a quadratic-form or Fisher-ratio bound) that a 0.05% SNR change limits parameter shifts to a negligible fraction of the quoted uncertainties, or a direct test in which the cross-covariance is inflated by a plausible factor (say 10) and the joint analysis is rerun in approximate form to show that Omega_m and sigma_8 move by a negligible fraction of their error bars. This would directly address the scenario in which the halo-model estimate of the cross-covariance is deficient.
  2. [Sec. III C, Eq. (5)] The main importance-sampling weight is never given in closed form; Eq. (5) states only the correlation correction. Because the normalizing flows approximate the posterior densities of each analysis over the eight-dimensional subspace, the weight applied to base samples should be the other probe's likelihood, i.e., the flow density divided by the (matched) prior, and the target density of the weighted samples should be stated explicitly. As written, the description ('update the sample weights w using the likelihood at that location in parameter space from the other flow') is ambiguous about whether the prior is divided out. This matters because the two reverse-direction consistency checks in Fig. 6 and Appendix B validate the flows and the IS directions against each other but would not detect a common error in prior handling that affects both directions equally. I ask the authors to write down the exact target distribution and weight, including any prior ratio, and to confirm that the released code implements that formula.
minor comments (3)
  1. [Sec. III D] The stacked cluster goodness-of-fit degrades from chi2 = 35.6 (PTE ~ 0.12) for the clusters-only analysis to chi2 = 43.1 (PTE = 0.03) at the joint MAP; while the unbinned hierarchical likelihood is the operative statistic, one interpretive sentence on this 27-point Delta chi2 = 7.5 degradation would strengthen the 'adequate description' conclusion in Sec. III D.
  2. [Sec. IV C] The sentence 'For reference, the purely geometrical measurement using DES Supernovae is yet another 26% tighter...' lacks a citation at that point; the relevant DES supernovae reference should be cited where the comparison is made.
  3. [Sec. IV B] Given the adopted prior lower bound sum m_nu > 0.06 eV, the claim of a mild preference for nonzero neutrino mass (posterior peak at 0.09 eV, mean 0.14 eV) would be easier to evaluate if the paper also reported a summary such as the posterior probability above 0.1 eV or an equivalent quantification of the preference.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the joint analysis is a likelihood combination of independently calibrated SPT cluster and DES 3x2pt probes; the shared-systematic and cross-covariance treatments are explicit propagation steps, not fitted inputs relabeled as predictions.

full rationale

The central constraints (Omega_m=0.300 +/- 0.017, sigma8=0.797 +/- 0.026, S8=0.796 +/- 0.013) come from multiplying the DES Y3 3x2pt Gaussian likelihood (Eq. 1, as published in [7]) with the SPT cluster hierarchical likelihood (Eqs. 2-3, from [35,20]). Neither likelihood is defined in terms of the other's output: the SPT cluster mass calibration uses small-scale 1-halo shear profiles and external simulation-based MWL-Mhalo calibration, while DES 3x2pt uses large-scale two-point functions. The paper explicitly tests, rather than assumes, the two potential sources of dependence: Section III A computes SNR differences with and without cross-covariance (~3% for cluster-only; ~0.05% for the combined data vector), and Section III B plus Appendix A propagates the shared photo-z and shear calibration systematics via the correlation rho=-0.81 in Eq. (5), showing negligible impact on cosmology. No parameter is fitted to the headline result and then presented as a prediction; no uniqueness theorem or ansatz is imported from the authors' prior work to force the model choice. The residual concerns raised in Section III A — the stacked approximation, the neglected optical cleaning in the covariance estimate, and the extrapolation to the unbinned likelihood — are accuracy and validation limitations, not circularity. Against external benchmarks (Planck, ACT+BAO, DES Y1, eRASS1), the paper presents genuine two-probe cosmological constraints, so the derivation is self-contained.

Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The central results are measurements rather than derivations. The free parameters are the 52 astrophysical nuisance parameters, all marginalized, plus the measured correlation coefficient used to couple the two likelihoods. The load-bearing axioms are the simulation-calibrated halo mass function, nonlinear power spectrum, intrinsic alignment model, the hydrodynamic-simulation mass calibration, and the demonstrated negligibility of the cluster-3x2pt cross-covariance. No invented physical entities are introduced.

free parameters (3)
  • DES Y3 3x2pt nuisance parameters (29) = not quoted individually
    Shear calibration biases, photometric redshift biases, galaxy bias, intrinsic alignment amplitudes, and related systematics marginalized in the DES Y3 likelihood [7]. These are fitted to data and marginalize over model uncertainty.
  • SPT cluster observable-mass relation parameters (23) = not quoted individually
    Amplitude, mass slope, redshift evolution, intrinsic scatter, correlated scatter, and the weak-lensing mass bias bWL in the cluster likelihood [20,35]. Fitted to cluster abundance and lensing data.
  • Correlation coefficient rho between bWL and Delta z4_s = -0.81
    Estimated from Monte Carlo recalibration of the cluster lensing model while recording shear and photo-z systematics (Sec. III B). Used in Eq. (5) to correlate the shared lensing systematic between the two probes.
assumptions (7)
  • domain assumption Spatially flat Lambda CDM and wCDM models with massive neutrinos
    Assumed geometry and model throughout Section IV; the paper does not test curvature or alternative dark energy models.
  • domain assumption Tinker 2008 halo mass function
    Used in Eq. (3) to compute the cluster abundance from halo masses; calibrated to N-body simulations in the cited literature.
  • domain assumption halofit nonlinear matter power spectrum
    Used for the 3x2pt theory predictions and cluster lensing profiles, as in [31,32].
  • domain assumption TATT intrinsic alignment model
    Adopted for DES 3x2pt intrinsic alignment nuisance modeling, following [7,33].
  • domain assumption Hydrodynamic-simulation-calibrated MWL-Mhalo relation
    Cluster mass calibration depends on the synthetic cluster lensing calibrations of [47], propagated through the cluster likelihood [35].
  • domain assumption Prior on sum of neutrino masses [0.06, 0.6] eV
    Lower bound from neutrino oscillation measurements, upper bound a uniform prior choice (Sec. IV). The posterior peaks at 0.09 eV, only slightly above the prior edge.
  • domain assumption Negligibility of cross-covariance between cluster and 3x2pt datasets
    Sec. III A assumes independence after showing SNR changes of ~0.05% in a halo-model calculation. Load-bearing for the validity of summing the two likelihoods.

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Cite this review

Pith. "Pith review of Multiprobe Cosmology from the Abundance of SPT Clusters and DES Galaxy Clustering and Weak Lensing." pith.science (2026). https://pith.science/paper/XQ74TVMF

@misc{pith2026241207765,
  author       = {Pith},
  title        = {Pith review of: Multiprobe Cosmology from the Abundance of SPT Clusters and DES Galaxy Clustering and Weak Lensing},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XQ74TVMF}},
  note         = {Machine review of arXiv:2412.07765}
}
abstract

Cosmic shear, galaxy clustering, and the abundance of massive halos each probe the large-scale structure of the Universe in complementary ways. We present cosmological constraints from the joint analysis of the three probes, building on the latest analyses of the lensing-informed abundance of clusters identified by the South Pole Telescope (SPT) and of the auto- and cross-correlation of galaxy position and weak lensing measurements (3$\times$2pt) in the Dark Energy Survey (DES). We consider the cosmological correlation between the different tracers and we account for the systematic uncertainties that are shared between the large-scale lensing correlation functions and the small-scale lensing-based cluster mass calibration. Marginalized over the remaining $\Lambda$ cold dark matter ($\Lambda$CDM) parameters (including the sum of neutrino masses) and 52 astrophysical modeling parameters, we measure $\Omega_\mathrm{m}=0.300\pm0.017$ and $\sigma_8=0.797\pm0.026$. Compared to constraints from Planck primary cosmic microwave background (CMB) anisotropies, our constraints are only 15% wider with a probability to exceed of 0.22 ($1.2\sigma$) for the two-parameter difference. We further obtain $S_8\equiv\sigma_8(\Omega_\mathrm{m}/0.3)^{0.5}=0.796\pm0.013$ which is lower than the Planck measurement at the $1.6\sigma$ level. The combined SPT cluster, DES 3$\times$2pt, and Planck datasets mildly prefer a nonzero positive neutrino mass, with a 95% upper limit $\sum m_\nu<0.25~\mathrm{eV}$ on the sum of neutrino masses. Assuming a $w$CDM model, we constrain the dark energy equation of state parameter $w=-1.15^{+0.23}_{-0.17}$ and when combining with Planck primary CMB anisotropies, we recover $w=-1.20^{+0.15}_{-0.09}$, a $1.7\sigma$ difference with a cosmological constant. The precision of our results highlights the benefits of multiwavelength multiprobe cosmology.

Figures

Figures reproduced from arXiv: 2412.07765 by the authors.

Figure 1
Figure 1. FIG. 1. Constraints on Ω [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Joint constraints on the sum of neutrino masses [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Marginalized constraints on the sum of neutrino [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Constraints on the matter density, the amplitude of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Impact of the shared systematics in the lensing source [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Parameter constraints (68% and 95% credibility) in ΛCDM. Upper right triangle: The original SPT and DES analyses [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

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