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Cosmological analyses based on surveys of galaxy clusters observed throughthe Sunyaev-Zel'dovich (SZ) effect strongly rely on the mean pressure profileof the cluster population. A tension is currently observed between thecosmological constraints obtained from the analyses of the CMB primaryanisotropies and those from cluster abundance in SZ surveys. This discrepancymay be explained by a wrong estimate of the hydrostatic bias parameter thatlinks the hydrostatic mass to the true mass of galaxy clusters. However, avariation of both the amplitude and the shape of the mean pressure profilecould also explain part of this tension. We analyze the effects of amodification of this profile on the constraints of the $\sigma_8$ and$\Omega_m$ parameters through the analysis of the SZ power spectrum measured bythe $Planck$ collaboration. We choose two mean pressure profiles that arerespectively lower and higher than the one obtained from the observation ofnearby clusters by $Planck$. The selection of the parameters of these twoprofiles is based on the current estimates of the pressure and gas massfraction profile distributions at low redshift. The cosmological parametersfound for these two profiles are significantly different from the ones obtainedwith the $Planck$ pressure profile. We conclude that a ${\sim}15\%$ decrease ofthe amplitude of the mean normalized pressure profile would alleviate thetension observed between the constraints of $\sigma_8$ and $\Omega_m$ from theCMB and cluster analyses without requiring extreme values of the mass biasparameter.

Impact of the mean pressure profile of galaxy clusters on the cosmological constraints from the $Planck$ tSZ power spectrum