Redshift Evolution of the Nonlinear Two‐Point Correlation Function

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 Ωₘ 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 r₀ depends strongly on Ωₘ and Ω_ν, being slower in models with lower Ωₘ or higher Ω_ν. Measurements of ξ to higher redshifts can therefore be a potential discriminator of cosmological parameters. The evolution rate of r₀ for halos within a given model increases with time, passing the phase of fixed comoving clustering at z~ 1 to 3 toward the regime of stable clustering at z~ 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.