# Cluster counts. II. Tensions, massive neutrinos, and modified gravity

## TL;DR

This paper investigates whether extensions to the standard cosmological model, such as massive neutrinos and modified gravity, can resolve tensions between CMB and galaxy cluster observations, finding that neutrinos do not help but modified gravity shows potential.

## Contribution

The study introduces a simple modified gravity model with a non-standard growth index and analyzes its impact on cluster counts and tensions in cosmological data.

## Key findings

- Massive neutrinos do not alleviate the cluster-CMB tension.
- A modified gravity model can help break degeneracies in cluster data.
- Calibration close to standard value suggests need for new physics.

## Abstract

The $\Lambda$CDM concordance model is very successful at describing our Universe with high accuracy and few parameters. Despite its successes, a few tensions persist; most notably, the best-fit $\Lambda$CDM model, as derived from the Planck CMB data, largely overpredicts the abundance of SZ clusters when using their standard mass calibration. Whether this is a sign of an incorrect calibration or the need for new physics remains a matter of debate. Here we examined two simple extensions of the standard model and their ability to release this tension: massive neutrinos and a simple modified gravity model via a non-standard growth index $\gamma$. We used both the Planck CMB and SZ cluster counts as datasets, with or without local X-ray clusters. In the case of massive neutrinos, the SZ calibration $(1-b)$ is constrained to $0.59^{+0.03}_{-0.04}$ (68\%), more than 5$\sigma$ away from its standard value $\sim0.8$. We found little correlation between $\sum m_\nu$ and $(1-b)$, corroborating previous conclusions derived from X-ray clusters; massive neutrinos do not alleviate the cluster-CMB tension. With our simple $\gamma$ model, we found a large correlation between calibration and growth index but contrary to local X-ray clusters, SZ clusters are able to break the degeneracy between the two thanks to their extended $z$ range. The calibration $(1-b)$ was then constrained to $0.60^{+0.05}_{-0.07}$, leading to an interesting constraint on $\gamma=0.60\pm 0.13$. When both massive neutrinos and modified gravity were allowed, preferred values remained centred on standard $\Lambda$CDM values, but $(1-b)\sim0.8$ was allowed (though only at the $2\sigma$ level) provided $\sum m_\nu\sim0.34 $ eV and $\gamma\sim0.8$. We conclude that massive neutrinos do not relieve the cluster-CMB tension and that a calibration close to the standard value $0.8$ would call for new physics in the gravitational sector.