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

An abstract should be given 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 a fraction of hot particles (massive neutrino) additional to 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 ∆T/T spectrum, and therefore should be ruled out. The models with a non-zero cosmological constant are in better agreement with the observations. We estimate the free cosmological parameters in ΛMDM with a negligible abundance of gravitational waves, and find that within the parameter ranges fν ≡ Ων/Ωm ∈ (0, 0.2), h ∈ (0.6, 0.7), and n ∈ (0.9, 1.1), (i) ΩΛ is strongly affected by a small fraction of hot matter, 0.45 < ΩΛ < 0.7 (1σ CL), and (ii) the cluster evolution test alone reveals the following explicit correlation between ΩΛ and fν : ΩΛ + 0.5fν = 0.65± 0.1.