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 Ω_M ≃ 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 Ω_M ≃ 1 and Γ ≃ 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.