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 _ { 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 \Gamma 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 _ { 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 .