Closing up the cluster tension?

TL;DR

This study investigates the apparent tension between high-redshift CMB measurements and low-redshift cluster counts in the $\sigma_8$ parameter within the $\Lambda$CDM model, finding no tension when calibrations are free but highlighting issues with standard cluster mass calibrations.

Contribution

It provides a direct low-redshift determination of $\sigma_8$ and assesses cluster mass calibrations without relying on high-redshift extrapolations, revealing consistency with CMB data but tension with standard calibrations.

Findings

No tension between CMB and low-redshift $f\sigma_8$ measurements when calibrations are free.

Standard cluster mass calibrations are inconsistent with combined cosmological data.

Calibrations of X-ray and SZ cluster masses are tightly constrained and align with CMB-based estimates.

Abstract

The excellent measurements of the cosmic microwave background (CMB) fluctuations by Planck allow us to tightly constrain the amplitude of matter fluctuations at redshift $\sim 1100$ in the $\Lambda$-cold dark matter ($\Lambda$CDM) model. This amplitude can be extrapolated to the present epoch, yielding constraints on the value of the $\sigma_8$ parameter. On the other hand, the abundance of Sunyaev-Zeldovich (SZ) clusters detected by Planck, with masses inferred using a hydrostatic equilibrium assumption, leads to a significantly lower value of the same parameter. This discrepancy is often dubbed the $\sigma_8$ tension in the literature and is sometimes regarded as a possible sign of new physics. Here, we examine a direct determination of $\sigma_8$ at the present epoch in $\Lambda$CDM, and thereby the cluster mass calibrations using cosmological data at low redshift, namely the measurements of $f\sigma_8$ from the analysis of the completed Sloan Digital Sky Survey (SDSS). We combined redshift-space distortion measurements with Planck CMB constraints, X-ray, and SZ cluster counts within the $\Lambda$CDM framework, but leaving the present-day amplitude of matter fluctuations as an independent parameter (i.e. no extrapolation is made from high-redshift CMB constraints). The calibration of X-ray and SZ masses are left as free parameters throughout the whole analysis. Our study yields tight constraints on the aforementioned calibrations, with values entirely consistent with results obtained from the full combination of CMB and cluster data only. Such an agreement suggests an absence of tension in the $\Lambda$CDM model between CMB-based estimates of $\sigma_8$ and constraints from low-redshift on $f\sigma_8$; however, it also indicates tension with the standard calibration of clusters masses.