  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_matter ~ 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_matter ~ 1 and Gamma ~ 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.
