The number density of quasars as a probe of initial power spectrum on small scale

The dependence of the number density of the bright QSOs at different redshifts ($n_{QSO}(z)$) on initial power spectrum is studied. It is assumed that QSO phenomenon is an early short term stage of evolution of massive galaxies with $M\ge 2\times {10}^{11}{h}^{-1}{M}_{\odot }$. The duration of such QSO stage which is passed through by fraction $\alpha$ of galaxies is determined by means of minimization of the divergence of the theoretical number density of QSOs at different redshifts for specified initial spectrum from observable one \cite{sc91}. It is shown that the nearest number densities of QSOs at $0.7\le z\le 3.5$ to observable ones are obtained for the tilted CDM model (${\mathrm{\Omega }}_b=0.1$, $n=0.7$). The QSO stage lasts $\sim 7\times {10}^7\mathrm{/}\alpha$ years and begins soon after the moment of rise of the first counterflow in collisionless component and shock wave in gas. The possibility of the reconstruction of initial power spectrum on small scale on the base of the observable data on number density of QSOs at different $z$ is considered too. Such reconstructed spectrum in comparison with standard CDM has steep reducing of power at $k\ge 0.5hMp{c}^{-1}$.