The Ω0Dependence of the Evolution of ξ(r)

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Abstract
The evolution of the two-point correlation function, ξ(r, z), and the pairwise velocity dispersion, σ(r, z), for both the matter, ξρρ, and halo population, ξhh, in three different cosmological models, (Ω0, λ0) = (1, 0), (0.2, 0), and (0.2, 0.8), are described. If the evolution of ξ is parameterized by ξ(r, z) = (1 + z)-(3+)ξ(r, 0), where ξ(r, 0) = (r/r0)-γ, then ρρ ranges from 1.04 ± 0.09 for (1, 0) and 0.18 ± 0.12 for (0.2, 0), as measured by the evolution of ξρρ at 1 Mpc (from z ~ 5 to the present epoch). For halos, depends indeed on their mean overdensity. Halos with a mean overdensity of ~2000 were used to compute the halo two-point correlation function, ξhh, tested with two different group-finding algorithms: the friends of friends algorithm and the spherical overdensity algorithm. It is certainly believed that the rate of growth of this ξhh will give a good estimate of the evolution of the galaxy two-point correlation function, at least from z ~ 1 to the present epoch. The values we get for hh range from 1.54 for (1, 0) to -0.36 for (0.2, 0), as measured by the evolution of ξhh from z ~ 1.0 to the present epoch. These values could be used to constrain the cosmological scenario. The evolution of the pairwise velocity dispersion for the mass and halo distribution is measured and compared with the evolution predicted by the cosmic virial theorem (CVT). According to the CVT, σ(r, z)2 ~ GQρ(z)r2ξ(r, z), or σ ∝ (1 + z)-/2. The values of measured from our simulated velocities differ from those given by the evolution of ξ and the CVT, keeping γ and Q constant: = 1.78 ± 0.13 for (1, 0) or = 1.40 ± 0.28 for (0.2, 0).

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