Abundance and evolution of galaxy clusters in cosmological models with massive neutrino

The time evolution of the number density of galaxy clusters and their mass and temperature functions are used to constrain cosmological parameters in the spatially flat dark matter models containing hot particles (massive neutrino) as well as cold and baryonic matter. We test the modified MDM () models with cosmic gravitational waves and show that they neither pass the cluster evolution test nor reproduce the observed height of the first acoustic peak in spectrum, and therefore should be ruled out. The models with a non-zero cosmological constant are in better agreement with observations. We estimate the free cosmological parameters in ΛMDM with a negligible abundance of gravitational waves, and find that within the parameter ranges , , , (i) the value of is strongly affected by a small fraction of hot dark matter: ( CL), and (ii) the redshift evolution of galaxy clusters alone reveals the following explicit relation between and : This degeneracy is also expected in LSS tests (with a smaller error). The present accuracy of observational data allows to bound the fraction of hot matter, ; the number of massive neutrino species remains undelimited, .