Spatial correlation function of quasars and power spectrum of cosmological matter density perturbations

Abstract

We examine the dependence of the spatial two-point correlation function of quasars $ξ_{qq}(r,z)$ at different redshifts on the initial power spectrum in flat cosmological models. Quasars and other elements of the large-scale structure of the universe are supposed to form in the peaks of the scalar Gaussian field of density fluctuations of appropriate scales. Quasars are considered as a manifestation of short-term active processes at the centers of these fluctuations. We propose a method for calculating the correlation function $ξ_{qq}(r,z)$ and show its amplitude and slope to depend on the shape of the initial power spectrum and the scale R of the fluctuations in which quasars are formed. We demonstrate that in the CDM models with the initial power spectrum slope $n=0.7\div1$ it is possible to explain, by choosing appropriate values of R, how the amplitudes and correlation radii of $ξ_{qq}(r,z)$ may either increase or decrease with increasing redshift z. In particular, the correlation radii of $ξ_{qq}(r,z)$ grow from $6-10h^{-1}$ Mpc when R grows from $0.45 h^{-1}$ to $1.3h^{-1}$ Mpc. The H+CDM model at realistic values of R fails to account for the observational data according to which the $ξ_{qq}(r,z)$ amplitude decreases with increasing $z$.