COLD PLUS HOT DARK-MATTER AND STRUCTURE FORMATION OF THE UNIVERSE

Cold plus hot (neutrino) dark matter models are studied and compared w ith the tilted cold dark matter models (which have a non-Zel'dovich in itial density perturbation spectrum). For the hybrid dark matter model s, a simpler treatment for the relativistic neutrinos is presented. Th e numerical results of this treatment are shown to be in good agreemen t with those given by other authors. Comparing the theoretical and the observational results of the quadrupole fluctuations of the cosmic ba ckground radiation and the large-scale velocity field of galaxies, the hybrid dark matter models require a fraction of neutrino density OMEG A(nu) congruent-to 0.3, a fraction of cold dark matter OMEGA(c) congru ent-to 0.7 and a number of massive neutrino species N(nu) = 1 for the case of Hubble's constant H-0 = 50 km s-1 Mpc-1. The distribution of c omoving number density of quasars at high redshifts is studied using t he Press-Schechter theory. The calculations show that the hybrid dark matter model (OMEGA(c) congruent-to 0.7, OMEGA(nu) congruent-to 0.3) a nd the tilted CDM model with n = 0.7 approximately 0.8 both account fo r the observed quasar abundance at high redshift.