Closing up the cluster tension?

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 ∼1100 in the Λ-cold dark matter (ΛCDM) model. This amplitude can be extrapolated to the present epoch, yielding constraints on the value of the σ8 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 σ8 tension in the literature and is sometimes regarded as a possible sign of new physics. Here, we examine a direct determination of σ8 at the present epoch in ΛCDM, and thereby the cluster mass calibrations using cosmological data at low redshift, namely the measurements of fσ8 from the analysis of the completed Sloan Digital Sky Survey. We combined redshift-space distortion measurements with Planck CMB constraints, X-ray, and SZ cluster counts within the ΛCDM 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 ΛCDM model between CMB-based estimates of σ8 and constraints from low-redshift on fσ8; however, it also indicates tension with the standard calibration of clusters masses.