On the baryon mass function for galaxy clusters

The evolution of the cluster abundance with redshift is known to be a powerful cosmological constrain when applied to X-ray clusters. Recently, the use of the evolution of the baryon mass function has been proposed as a new variant that is free of the uncertainties present in the Temperature-Mass relation. A flat model with Omega_matter ~ 0.3 was shown to be preferred in the case of a standard cold dark matter scenario. We have compared the high redshift predictions of the baryon mass in clusters for a more general class of spectra having a varying shape factor Gamma in models normalized to reproduce the local baryon mass function. We have found that models with Omega_matter ~ 1 and Gamma ~ 0.12 reproduce high redshift cluster data equally well as the concordance model and we conclude that the baryon mass function evolution on its own is not an efficiently discriminant among the more general family of flat cosmological models with non-standard power spectra