Evolution of galaxy clusters in ΛMDM cosmologies

The time evolution of galaxy cluster abundance is used to constrain cosmological parameters in dark matter models containing a fraction of hot particles (massive neutrino). We test the modified MDM models with cosmic gravitational waves which are in agreement with observational data at $z=0$, and show that they do not pass the cluster evolution test and therefore should be ruled out. The models with a non-zero cosmological constant are in better agreement with the evolution test. We estimate $\Omega_\Lambda$ and find that it is strongly affected by a small fraction of hot dark matter: $0.4 <\Omega_\Lambda <0.8$ for $\Omega_H /\Omega_M <0.2$.