Constraining cosmological models by the cluster mass function

We present a comparison between two observational mass functions and three theoretical mass functions for eight cosmological models suggested by the data from the recently completed BOOMERANG-98 and MAXIMA-1 cosmic microwave background (CMB) anisotropy experiments as well as from peculiar velocities (PVs) and Type Ia supernova (SN) observations. The cosmological models have been proposed as the best-fit models by several groups. We show that no model is in agreement with the abundances of X-ray clusters at similar to 10(14.)7 h(-1) M-circle dot. On the other hand, we find that the BOOM + MAX + COBE: I, Refined Concordance, and Lambda MDM models are in a good agreement with the abundances of optical clusters. The P11 model and especially the Concordance model predict slightly lower abundances than observed at similar to 10(14.)6 h(-1) M-circle dot. The BOOM + MAX + COBE: II and PV + CMB + SN models predict slightly higher abundances than observed at similar to 10(14.9) h(-1) M-circle dot. The nonflat MAXIMA-1 is in a fatal conflict with the observational cluster abundances and can be safely ruled out.