Closing up the cluster tension?

¹ Université de Toulouse, UPS-OMP, IRAP and CNRS, IRAP, 14, Avenue Edouard Belin, 31400 Toulouse, France
e-mail: alain.blanchard@irap.omp.eu
² Université PSL, Observatoire de Paris, Sorbonne Université, CNRS, LERMA, 75014 Paris, France
e-mail: stephane.ilic@obspm.fr
³ Université de Paris, CNRS, Astroparticule et Cosmologie, 75013 Paris, France

Received: 1 April 2021
Accepted: 15 September 2021

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.