The Lambda cold dark matter (ΛCDM) 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 ΛCDM 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 γ. 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+0.031−0.037 (68% limits), more than 5σ away from its standard value (1 − b)∼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 γ model, we found a large correlation between the calibration and the growth index γ, 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+0.053−0.065, leading to an interesting constraint on γ = 0.60 ± 0.13. When both massive neutrinos and modified gravity were allowed, preferred values remained centred on standard ΛCDM values, but a calibration (1 − b)∼0.8 was allowed (though only at the 2σ level) provided ∑mν ∼ 0.34 eV and γ ∼ 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)∼0.8 would call for new physics in the gravitational sector.
Modified gravity with massive neutrinos as a testable alternative cosmological model