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

The Lambda cold dark matter (Lambda CDM) concordance model is very successful at describing our Universe with high accuracy and only a few parameters. Despite its successes, a few tensions persist; most notably, the best-fit Lambda CDM model, as derived from the Planck cosmic microwave background (CMB) data, largely overpredicts the abundance of Sunyaev-Zel'dovich (SZ) clusters when using their standard mass calibration. Whether this is the sign of an incorrect calibration or the need for new physics remains a matter of debate. In this study, we examined two simple extensions of the standard model and their ability to release the aforementioned tension: massive neutrinos and a simple modified gravity model via a non-standard growth index gamma. We used both the Planck CMB power spectra and SZ cluster counts as datasets, alone and in combination with local X-ray clusters. In the case of massive neutrinos, the cluster-mass calibration (1-b) is constrained to 0.585(-0.037)(+0.031) (68% limits), more than 5 sigma away from its standard value (1 - b) similar to 0.8. We found little correlation between neutrino masses and cluster calibration, 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 the calibration and the growth index gamma, but contrary to local X-ray clusters, SZ clusters are able to break the degeneracy between the two parameters thanks to their extended redshift range. The calibration (1-b) was then constrained to 0.602(-0.065)(+0.053), leading to an interesting constraint on gamma = 0.60 +/- 0.13. When both massive neutrinos and modified gravity were allowed, preferred values remained centred on standard Lambda CDM values, but a calibration (1-b) similar to 0.8 was allowed (though only at the 2 sigma level) provided Sigma m(nu) similar to 0.34 eV and gamma similar to 0.8. We conclude that massive neutrinos do not relieve the cluster-CMB tension, and that a calibration close to the standard value (1-b) similar to 0:8 would call for new physics in the gravitational sector.