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REVIEW 2 major objections 3 minor 106 references

Interacting Dark Sector (ETHOS $n=0$): Cosmological Constraints from SPT Cluster Abundance with DES and HST Weak Lensing Data

T0 review · 2 major / 3 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Using 1,005 South Pole Telescope clusters with DES and HST weak-lensing masses, the paper bounds the interacting dark-radiation temperature ratio to below 10% when combined with CMB and BAO data.

desk verdict First real cluster-abundance limit on ETHOS n=0, carefully done, but the quoted xi_DR bound depends on an unvalidated halo mass function mapping that could shift the result. read the letter →

arxiv 2411.19911 v2 pith:UZ3VH4SD submitted 2024-11-29 astro-ph.CO

A. Mazoun , S. Bocquet , J. J. Mohr , M. Garny , H. Rubira , M. Klein , L. E. Bleem , S. Grandis
show 59 more authors
T. Schrabback M. Aguena S. Allam S. W. Allen O. Alves F. Andrade-Oliveira D. Brooks A. Carnero Rosell M. Carrasco Kind J. Carretero M. Costanzi L. N. da Costa T. M. Davis S. Desai J. De Vicente H. T. Diehl S. Dodelson P. Doel S. Everett B. Flaugher J.Frieman J.Garcia-Bellido R.Gassis G.Giannini D.Grün G.Gutierrez S.R.Hinton D. L. Hollowood D. J. James K. Kuehn O. Lahav S. Lee M. Lima G. Mahler J. L. Marshall R. Miquel J. Myles R. L. C. Ogando M. E. S. Pereira A. Pieres A. A. Plazas Malagón A. Porredon C. L. Reichardt A. K. Romer S. Samuroff E. Sanchez D. Sanchez Cid I. Sevilla-Noarbe M. Schubnell M. Smith E. Suchyta M. E. C. Swanson A. Tamosiunas G. Tarle D. L. Tucker V. Vikram N. Weaverdyck J. Weller P. Wiseman
This is my paper · ORCID
classification astro-ph.CO
keywords interactingdarkmatterradiationETHOSgalaxyclusterabundanceweaklensingmasscalibrationSunyaev-ZeldovicheffectsectorcosmologyS8tension
topics Dark Matter
open problems Dark Matter
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

This paper asks how much dark matter can interact with a bath of dark radiation without changing the number of galaxy clusters that form. Using 1,005 Sunyaev-Zeldovich-selected clusters from the South Pole Telescope with masses calibrated by DES Year 3 and HST weak-lensing data, the authors compare the observed abundance to the predictions of an interacting dark-matter–dark-radiation model (ETHOS $n=0$). They obtain an upper limit on the dark-radiation-to-CMB temperature ratio of $\xi_{\rm DR}<0.166$ at 95% credibility from clusters alone, tightening to $\xi_{\rm DR}<0.098$ when Planck 2018 CMB and BOSS BAO data are added, roughly three times tighter than CMB+BAO alone. If correct, this would be the strongest cluster-based constraint on interacting dark radiation and would leave room for such interactions to ease the $S_8$ tension, with a weak preference for a small nonzero $\xi_{\rm DR}$.

What carries the argument

The load-bearing machinery is the ETHOS perturbation system for a tightly coupled dark-matter–dark-radiation fluid, in which the Euler equation for the interacting dark matter carries a drag term $\Gamma_{\rm IDM-DR}(\theta_{\rm IDM}-\theta_{\rm DR})$ with $\Gamma_{\rm IDM-DR}(z)\propto(1+z)$ for $n=0$, while the dark radiation is treated as a self-interacting fluid with zero shear stress. This drag damps density perturbations on a wide range of scales, with $\xi_{\rm DR}$ setting where the suppression begins. The cluster abundance likelihood of Eq. (24) then maps the halo mass function, computed from the CLASS linear power spectrum for this model, into predicted counts in tSZE significance, richness, weak-lensing shear, and redshift, with the observable–mass relations calibrated empirically by DES Y3 and HST weak-lensing data.

What would settle it

A cosmological N-body simulation suite evolving the ETHOS $n=0$ model with $f_{\rm IDM}=10\%$ and tight coupling, comparing its halo mass function to the Tinker/emulator prediction used in Eq. (24), would settle the central claim: if cluster counts differ by more than the analysis's systematic error budget, the $\xi_{\rm DR}$ upper limits are biased.

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Extended reading notes

Core claim

The paper's central claim is that weak-lensing-calibrated galaxy cluster abundance is sharply sensitive to the temperature ratio $\xi_{\rm DR}=T_{\rm DR}/T_{\rm CMB}$ in ETHOS $n=0$ interacting dark-matter–dark-radiation models, and that this sensitivity produces the tightest existing upper limit on that ratio. Within the microscopically motivated $SU(N)$ dark-sector realization, a fraction $f_{\rm IDM}=10\%$ of the dark matter is tightly coupled to a self-interacting dark-radiation fluid, and the interaction suppresses the matter power spectrum over a broad range of scales whose onset is set by $\xi_{\rm DR}$. The paper reports $\xi_{\rm DR}<0.166$ at 95% credibility from SPT clusters with DES Y3 and HST masses alone, and $\xi_{\rm DR}<0.098$ when combined with Planck 2018 and BOSS BAO data, corresponding in an $SU(3)$ realization to $\Delta N_{\rm eff}<0.003$. It also finds $S_8=0.793\pm0.032$ from clusters alone and a mild, statistically insignificant preference for nonzero $\xi_{\rm DR}$ that persists across analysis choices, which the authors interpret as leaving a physical route toward resolving the $S_8$ tension.

Load-bearing premise

The result rests on assuming that the dark-matter–dark-radiation power suppression maps directly onto the standard gravity-only halo mass function, a mapping that this paper does not check with simulations.

Editorial extensions

If this is right

  • SPT cluster counts alone constrain $\xi_{\rm DR}<0.166$ at 95% credibility, demonstrating that cluster abundance is a competitive standalone probe of interacting dark radiation.
  • Adding Planck 2018 and BOSS BAO data tightens this to $\xi_{\rm DR}<0.098$, which for a minimal $SU(3)$ dark sector corresponds to $\Delta N_{\rm eff}<0.003$, about three times stronger than the CMB+BAO-only bound.
  • Cluster abundance is most sensitive to scales $k\in[0.02,0.08]\,h/\mathrm{Mpc}$, making it complementary to small-scale probes for testing the full ETHOS parameter space.
  • The measured $S_8=0.793\pm0.032$ is consistent with both Planck and cosmic-shear measurements, and the posterior retains a tail toward lower values, leaving room to address the $S_8$ tension.
  • Marginalizing over neutrino mass shows no degeneracy with $\xi_{\rm DR}$ and yields $\sum m_\nu<0.096$ eV from clusters+CMB+BAO, tighter than CMB+BAO alone.

Reading between the lines

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

  • A direct test of the central assumption would be N-body simulations of the ETHOS $n=0$ model; if the simulated halo mass function deviates from the Tinker/emulator prediction by more than the analysis's systematic budget, the reported $\xi_{\rm DR}$ limits would be biased.
  • Combining cluster abundance with cosmic-shear measurements should break the degeneracy between $\xi_{\rm DR}$ and the interaction parameters $f_{\rm IDM}$ and $a_{\rm dark}$, which cluster counts alone cannot constrain.
  • An independent cluster sample selected at other frequencies or wavelengths could confirm or refute the mild preference for nonzero $\xi_{\rm DR}$, since that preference is currently based on one dataset combination.
  • If the preference is physical, the same model predicts a characteristic scale-dependent shape change in the halo mass function that future lensing-calibrated cluster surveys should detect as a deviation from $\Lambda$CDM at the few-percent level.
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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. The paper derives cosmological constraints on the ETHOS n=0 interacting dark matter–dark radiation (IDM–DR) model using the abundance of 1,005 SPT clusters with weak-lensing mass calibration from DES Y3 and HST. The key result is an upper limit on the dark radiation temperature ratio, ξ_DR < 0.166 at 95% credibility from SPT clusters × WL alone, and ξ_DR < 0.098 at 95% credibility when combined with Planck 2018 CMB and BOSS BAO data. In an SU(3) realization this corresponds to ΔN_eff < 0.003 for tightly coupled, fluid-like dark radiation. The paper also examines the impact of massive neutrinos, verifies robustness to freeing f_IDM and a_dark (Appendix A), and reports a statistically insignificant preference for non-zero ξ_DR. The analysis pipeline is the same validated cluster-abundance and mass-calibration framework used in recent SPT/DES work, with the IDM–DR matter power spectrum computed by CLASS.

Significance. If the underlying modeling assumption holds, this is a significant result: it would be the tightest cluster-abundance constraint on interacting dark radiation and demonstrates that tSZE cluster counts with weak-lensing mass calibration provide a probe complementary to CMB and BAO for ETHOS-type dark sectors. The paper is careful and honest in reporting: the Poisson abundance likelihood is well established, the weak-lensing mass calibration is anchored to external hydrodynamical simulations, Appendix A explicitly tests freedom in adark and fIDM, and the neutrino-mass check in Sec. V.B is a useful robustness test. The main caveat is that the central bound is obtained by feeding the CLASS linear power spectrum into a gravity-only Tinker/emulator halo mass function without a dedicated validation for the IDM–DR model; this is a load-bearing assumption that needs to be addressed before the quoted limits can be taken at face value.

major comments (2)
  1. [Sec. IV.B–IV.C, Eq. (24)] The central ξ_DR constraints assume that the halo mass function for the IDM–DR model is obtained by inserting the CLASS linear matter power spectrum into the standard gravity-only Tinker/emulator HMF. This is not obviously valid when 10% of the DM is tightly coupled to a dark radiation fluid: in that regime the IDM component is pressure-supported and may not participate in halo collapse on cluster scales, so the total-matter σ(M) is not an established collapse variable for this model. A 10–20% bias in dN/dM at M ~ 3×10^14 h^-1 Mpc could shift the 95% upper limits by an amount comparable to the improvement claimed from adding clusters to CMB+BAO. Appendix A varies adark and fIDM within the same unvalidated HMF framework, so it does not test this assumption. I request either a simulation-based validation of the HMF mapping (e.g., N-body or calibrated emulator tests) or an explicit conservative systematic term folded into the reported limits.
  2. [Sec. IV.A, Eq. (19)] The MWL–Mhalo relation used for weak-lensing mass calibration is calibrated to standard CDM hydrodynamical simulations and assumed unchanged in the IDM–DR model. However, the IDM–DR power suppression alters the concentration–mass relation of collapsed halos, and the NFW-derived lensing mass bias MWL/M200c may differ from the CDM-calibrated value. Since the abundance likelihood is very sensitive to the absolute mass scale, a few-percent shift in this bias could bias ξ_DR and also contribute to the reported slight preference for non-zero ξ_DR. The paper should quantify the expected change in the mass calibration for IDM–DR halos, or at least provide an estimate of the resulting systematic uncertainty on the ξ_DR limits.
minor comments (3)
  1. [Abstract and Sec. VI] The abstract states that the combined limit is 'around three times tighter' while Sec. VI says the ξ_DR bound itself is '30% tighter'; both statements are correct because the DR energy density scales as ξ_DR^4, but the wording is easy to misread. Please state explicitly which quantity (ξ_DR versus ΔN_eff or ρ_DR) is improved by which factor.
  2. [Sec. V.A and Fig. 3] The non-standard combination S8^opt = σ8(Ωm/0.3)^0.2 is defined in the figure caption and Table II, but it would help to define it in the main text at first use, since most readers will expect the standard S8 exponent of 0.5.
  3. [Sec. V.A] The 'slight preference for a non-zero value of ξ_DR' is described as robust to several variations, but no Bayes factor or other model-comparison statistic is reported. A posterior mode away from zero is not by itself evidence for the model; please add a quantitative model comparison or explicitly label the statement as a posterior-only hint.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the ξDR constraints are genuine fits to external cluster and lensing data.

full rationale

The central result, ξDR < 0.166 from SPT-clusters×WL and ξDR < 0.098 from SPT-clusters×WL+CMB+BAO, is obtained by evaluating the Poisson cluster abundance likelihood in Eqs. (23)–(24) with the ETHOS n=0 IDM-DR linear matter power spectrum from CLASS and the standard gravity-only Tinker/emulator halo mass function. The observable–mass relations (Eqs. 15, 18, and 19) are calibrated simultaneously from the DES Y3 and HST weak-lensing data, with priors anchored to external hydrodynamical simulations (Magneticum and IllustrisTNG), not to the IDM-DR model being tested. The parameter ξDR is a free parameter of the likelihood and the quoted 95% bounds are the marginalized posteriors; no fitted parameter is renamed as a prediction. The fixed choices fIDM = 0.1 and log10[adark/Mpc^-1] = 8 are adopted from the authors' prior work [46], but Appendix A shows the ξDR constraint is robust to allowing these parameters to vary, so this self-citation is not load-bearing. The unvalidated mapping from the linear power spectrum to the halo mass function is a possible source of systematic bias, but it is not circular: the HMF calibration is external and the derived limit is not identical to any input by construction.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central constraint on ξ_DR is a data fit, so ξ_DR is listed as a fitted parameter, and the hand-chosen fixed values f_IDM = 0.1 and a_dark = 10^8 Mpc^-1 are also listed as free parameters because they are chosen rather than constrained. The analysis rests on the ETHOS model equations, the universal halo mass function assumption, the simulated mass calibration priors, and the DR fluid approximation, all of which are recorded as axioms. No new entities are introduced by this paper.

free parameters (3)
  • ξ_DR = < 0.098 (95% CI upper limit, combined)
    DR temperature ratio; free parameter with flat prior U(0.001, 0.5), constrained by the data.
  • f_IDM = 0.1 (fixed)
    Fraction of interacting dark matter; fixed to 0.1 by hand, shown to have weak impact on the halo mass function within the cluster mass range.
  • log10(a_dark / Mpc^-1) = 8 (fixed)
    Interaction strength; fixed to the tight coupling limit by hand; results are insensitive to this value in the target regime.
assumptions (6)
  • domain assumption ETHOS n=0 IDM-DR perturbation equations and interaction rate Γ ∝ (1+z)
    Eqs. (5), (6), (7), (8) and the rate in Sec. II are taken from the ETHOS framework and the SU(N) dark sector model; they map ξ_DR and f_IDM to the matter power spectrum.
  • domain assumption Universal gravity-only halo mass function applied to IDM-DR linear power spectrum
    Eq. (24) uses the standard HMF formalism with the IDM-DR linear matter power spectrum from CLASS; the validity of this mapping is assumed, not demonstrated with simulations in this paper.
  • domain assumption Weak-lensing mass calibration priors from Magneticum and Illustris TNG
    Sec. IV.A: the MWL-Mhalo relation and scatter are calibrated using hydrodynamical simulations, and the analysis assumes these priors capture baryonic effects with the quoted systematic uncertainty.
  • ad hoc to paper Tight coupling limit and fixed f_IDM = 0.1
    Sec. IV.C fixes log10(a_dark/Mpc^-1) = 8 and f_IDM = 0.1, justified by forecast insensitivity of the HMF to these parameters; Appendix A checks robustness.
  • domain assumption DR fluid approximation with zero shear
    Eqs. (7)-(8) treat DR as a perfect fluid with σ_DR = 0, consistent with a self-interacting non-Abelian gauge sector in the SU(N) model.
  • domain assumption Standard flat ΛCDM background with DR and Planck-based Gaussian priors for cluster-only analysis
    Sec. IV.C applies Gaussian priors on Ωb h^2 and n_s from Planck and a wide prior on h for the cluster-only case; the background includes the additional DR density.

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Pith. "Pith review of Interacting Dark Sector (ETHOS $n=0$): Cosmological Constraints from SPT Cluster Abundance with DES and HST Weak Lensing Data." pith.science (2026). https://pith.science/paper/UZ3VH4SD

@misc{pith2026241119911,
  author       = {Pith},
  title        = {Pith review of: Interacting Dark Sector (ETHOS $n=0$): Cosmological Constraints from SPT Cluster Abundance with DES and HST Weak Lensing Data},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UZ3VH4SD}},
  note         = {Machine review of arXiv:2411.19911}
}
abstract

We use galaxy cluster abundance measurements from the South Pole Telescope (SPT) enhanced by Multi-Component Matched Filter (MCMF) confirmation and complemented with mass information obtained using weak-lensing data from Dark Energy Survey Year~3 (DES Y3) and targeted Hubble Space Telescope (HST) observations for probing deviations from the cold dark matter paradigm. Concretely, we consider a class of dark sector models featuring interactions between dark matter (DM) and a dark radiation (DR) component within the framework of the Effective Theory of Structure Formation (ETHOS). We focus on scenarios that lead to power suppression over a wide range of scales, and thus can be tested with data sensitive to large scales, as realized for example for DM$-$DR interactions following from an unbroken non-Abelian $SU(N)$ gauge theory (interaction rate with power-law index $n=0$ within the ETHOS parameterization). Cluster abundance measurements are mostly sensitive to the amount of DR interacting with DM, parameterized by the ratio of DR temperature to the cosmic microwave background (CMB) temperature, $\xi_{\rm DR}=T_{\rm DR}/T_{\rm CMB}$. We find an upper limit $\xi_{\rm DR}<17\%$ at $95\%$ credibility. When the cluster data are combined with Planck 2018 CMB data along with baryon acoustic oscillation (BAO) measurements we find $\xi_{\rm DR}<10\%$, corresponding to a limit on the abundance of interacting DR that is around three times tighter than that from CMB+BAO data alone. We also discuss the complementarity of weak lensing informed cluster abundance studies with probes sensitive to smaller scales, explore the impact on our analysis of massive neutrinos, and comment on a slight preference for the presence of a non-zero interacting DR abundance, which enables a physical solution to the $S_8$ tension.

Figures

Figures reproduced from arXiv: 2411.19911 by the authors.

Figure 1
Figure 1. FIG. 1. The distribution of clusters and contaminating sources from the SPT surveys [ [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Average matter profiles ∆Σ( [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Posteriors obtained from analyzing the IDM [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Comparison between the combined posteriors ob [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Variance (1 [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Posteriors of IDM [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Posterior distribution of all parameters with a flat prior employed in the analysis of SPT-clusters [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]

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Pith tools

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