Cosmological implications of a modified galaxy cluster pressure profile using the $Planck$ tSZ power spectrum

The mean pressure profile of the cluster population is a key element in cosmological analyses based on surveys of galaxy clusters observed through the Sunyaev-Zel'dovich (SZ) effect. A variation of both the shape and the amplitude of this profile could explain part of the discrepancy currently observed between the cosmological constraints obtained from the analyses of the CMB primary anisotropies and those from cluster abundance in SZ surveys for a fixed mass bias parameter. We study the cosmological implications of a modification of the mean pressure profile through the analysis of the SZ power spectrum measured by $Planck$. We define two mean pressure profiles on either side of the one obtained from the observation of nearby clusters by $Planck$. The parameters of these profiles are chosen to ensure their compatibility with the distributions of pressure and gas mass fraction profiles observed at low redshift. We find significant differences between the cosmological parameters obtained by using these two profiles to fit the $Planck$ SZ power spectrum and those found in previous analyses. We conclude that a ${\sim}15\%$ decrease of the amplitude of the mean normalized pressure profile is sufficient to alleviate the discrepancy observed between the constraints of $\sigma_8$ and $\Omega_m$ from the CMB and cluster analyses.