Redshift Evolution of the Nonlinear Two-Point Correlation Function

This paper presents a detailed theoretical study of the two-point correlation function $\xi$ for both dark matter halos and the matter density field in five cosmological models with varying matter density $\Omega_m$ and neutrino fraction $\Omega_\nu$. The objectives of this systematic study are to evaluate the nonlinear gravitational effects on $\xi$, to contrast the behavior of $\xi$ for halos vs. matter, and to quantify the redshift evolution of $\xi$ and its dependence on cosmological parameters. Overall, $\xi$ for halos exhibits markedly slower evolution than $\xi$ 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 $\Omega_m$ and $\Omega_\nu$, being slower in models with lower $\Omega_m$ or higher $\Omega_\nu$. Measurements of $\xi$ 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 $\xi$, 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.