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

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