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 Ων . 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 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 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. To appear in the Astrophysical Journal (Vol. 510, January 1 1999) Subject headings: cosmology : theory – dark matter – elementary particles – galaxies: evolution – large-scale structure of universe – methods: numerical