Redshift Evolution of the Nonlinear Two-Point Correlation Function

Abstract

This paper presents a detailed theoretical study of the two-point correlation function $ξ$ for both dark matter halos and the matter density field in five cosmological models with varying matter density $Ω_m$ and neutrino fraction $Ω_ν$. The objectives of this systematic study are to evaluate the nonlinear gravitational effects on $ξ$, to contrast the behavior of $ξ$ for halos vs. matter, and to quantify the redshift evolution of $ξ$ and its dependence on cosmological parameters. Overall, $ξ$ for halos exhibits markedly slower evolution than $ξ$ for matter, and its redshift dependence is much more intricate than the single power-law parameterization used in the literature. Of particular interest is that the redshift evolution of the halo-halo correlation length $r_0$ depends strongly on $Ω_m$ and $Ω_ν$, being slower in models with lower $Ω_m$ or higher $Ω_ν$. Measurements of $ξ$ to higher redshifts can therefore be a potential discriminator of cosmological parameters. The evolution rate of $r_0$ for halos within a given model increases with time, passing the phase of fixed comoving clustering at $z\sim 1$ to 3 toward the regime of stable clustering at $z\sim 0$. The shape of the halo-halo $ξ$, on the other hand, is well approximated by a power law with slope -1.8 in all models and is not a sensitive model discriminator.