Cosmological Models by the Cluster Mass Function

We present a comparison between two observational and three theoretical mass functions for eight cosmological models suggested by the data from recently completed BOOMERANG-98, MAXIMA-1 cosmic microwave background (CMB) anisotropy experiments as well as peculiar velocities (PV) and Type Ia Supernovae (SN) observations. The cosmological models have been proposed as the best fit models by several groups. We show that all three theoretical mass functions make similar predictions. We find no model passed the cluster abundance test without a problem. The Concordance and Refined Concordance models show the best agreement with the cluster abundance test. The nonflat MAXIMA-1 and ΛMDM models are in a fatal conflict with the observational cluster abundances and can be safely ruled out. Other models have serious problems with the observational cluster mass function. Subject headings: cosmology:theory — cosmology:observation — galaxies: clusters: general — large-scale structure of universe