Redshift Evolution of the Nonlinear Two‐Point Correlation Function

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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 Ωm and neutrino fraction Ων. The objectives of this systematic study are to evaluate the nonlinear gravitational effects on ξ, to contrast the behavior of ξ for halos versus 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 Ων, being slower in models with lower Ωm or higher Ων. 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~1-3 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.
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