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We present a study of the weak lensing inferred matter profiles ΔΣ(R) of 698 South Pole Telescope (SPT) thermal Sunyaev-Zel’dovich effect (tSZE) selected and MCMF optically confirmed galaxy clusters in the redshift range 0.25 <  z <  0.94 that have associated weak gravitational lensing shear profiles from the Dark Energy Survey (DES). Rescaling these profiles to account for the mass dependent size and the redshift dependent density produces average rescaled matter profiles ΔΣ(R/R_200c)/(ρ_critR_200c) with a lower dispersion than the unscaled ΔΣ(R) versions, indicating a significant degree of self-similarity. Galaxy clusters from hydrodynamical simulations also exhibit matter profiles that suggest a high degree of self-similarity, with RMS variation among the average rescaled matter profiles with redshift and mass falling by a factor of approximately six and 23, respectively, compared to the unscaled average matter profiles. We employed this regularity in a new Bayesian method for weak lensing mass calibration that employs the so-called cluster mass posteriorP(M₂₀₀|ζ̂, λ̂,z), which describes the individual cluster masses given their tSZE (ζ̂) and optical (λ̂,z) observables. This method enables simultaneous constraints on richnessλ-mass and tSZE detection significanceζ-mass relations using average rescaled cluster matter profiles. We validated the method using realistic mock datasets and present observable-mass relation constraints for the SPT×DES sample, where we constrained the amplitude, mass trend, redshift trend, and intrinsic scatter. Our observable-mass relation results are in agreement with the mass calibration derived from the recent cosmological analysis of the SPT×DES data based on a cluster-by-cluster lensing calibration. Our new mass calibration technique offers a higher efficiency when compared to the single cluster calibration technique. We present new validation tests of the observable-mass relation that indicate the underlying power-law form and scatter are adequate to describe the real cluster sample but that also suggest a redshift variation in the intrinsic scatter of theλ-mass relation may offer a better description. In addition, the average rescaled matter profiles offer high signal-to-noise ratio (S/N) constraints on the shape of real cluster matter profiles, which are in good agreement with available hydrodynamical ΛCDM simulations. This high S/N profile contains information about baryon feedback, the collisional nature of dark matter, and potential deviations from general relativity. 

We present constraints on the $f\left(R\right)$gravity model using a sample of 1005 galaxy clusters in the redshift range 0.25–1.78 that have been selected through the thermal Sunyaev-Zel’dovich effect from South Pole Telescope data and subjected to optical and near-infrared confirmation with the multicomponent matched filter algorithm. We employ weak gravitational lensing mass calibration from the Dark Energy Survey Year 3 data for 688 clusters at $z<0.95$and from the Hubble Space Telescope for 39 clusters with $0.6<z<1.7$. Our cluster sample is a powerful probe of $f\left(R\right)$gravity, because this model predicts a scale-dependent enhancement in the growth of structure, which impacts the halo mass function (HMF) at cluster mass scales. To account for these modified gravity effects on the HMF, our analysis employs a semianalytical approach calibrated with numerical simulations. Combining calibrated cluster counts with primary cosmic microwave background temperature and polarization anisotropy measurements from the Planck 2018 release, we derive robust constraints on the $f\left(R\right)$parameter $f_{R0}$. Our results, ${\log }_{10}\left|f_{R0}\right|<-5.32$at the 95% credible level, are the tightest current constraints on $f\left(R\right)$gravity from cosmological scales. This upper limit rules out $f\left(R\right)$-like deviations from general relativity that result in more than a $\sim 20\%$enhancement of the cluster population on mass scales $M_{200\mathrm{c}}>3\times {10}^{14}{M}_{\odot }$. Published by the American Physical Society2025