The abundance of QSOs in various cold dark matter models

Based on the statistics of the peaks in the random Gaussian field, we put forward a method to model the evolution of quasars, which are assumed to be a phenomenon of the early stages for some massive galaxies. Our calculations show that the cold-hot mixed dark matter model with Omega(h) = 0.3 cannot match the observed quasar abundance at redshift z = 4.5, and other prevailing CDM models, such as the mixed dark matter model with Omega(h) = 0.2, the tilted CDM models with n = 0.7 or 0.8, and the flat Lambda CDM models with Omega(Lambda) = 0.6 or 0.7, are compatible with the observation of the abundance of QSOs on the range of z = 2-5.