The baryon mass function for galaxy clusters

Context.The evolution of the cluster abundance with redshift is known to be a powerful cosmological constraint when applied to X-ray clusters. Recently, 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 $\Omega_{\rm M} \simeq 0.3$ was shown to be preferred in the case of a standard cold dark matter scenario. Aims.We compared the high redshift predictions of the baryon mass in clusters with data for a more general class of spectra with a varying shape factor Γ without any restriction to the standard cold dark matter scenario in models normalized to reproduce the local baryon mass function. Methods.Using various halo mass functions existing in the literature we evaluated the corresponding baryon mass functions for the case of the non-standard power spectra mentioned previously. Results.We found that models with $\Omega_{\rm M} \simeq 1$ and $\Gamma \simeq 0.12$ reproduce high redshift cluster data just as well as the concordance model does. Conclusions.Finally, we conclude that the baryon mass function evolution alone does not efficiently discriminate between the more general family of flat cosmological models with non-standard power spectra