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 ^ { +0.031 } _ { -0.037 } ( 68 % limits ) , more than 5 \sigma away from its standard value ( 1 - b ) \sim 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 ^ { +0.053 } _ { -0.065 } , 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 a calibration ( 1 - b ) \sim 0.8 was allowed ( though only at the 2 \sigma level ) provided \sum m _ { \nu } \sim 0.34 eV and \gamma \sim 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 ) \sim 0.8 would call for new physics in the gravitational sector .