The Omega(0) dependence of the evolution of xi(r)

The evolution of the two-point correlation function, xi(r, z), and the pairwise velocity dispersion, sigma(r, z), for both the matter, xi(rho rho), and halo population, xi(hh), in three different cosmological models, (Omega(0), lambda(0))=(1, 0), (0.2, 0), and (0.2, 0.8), are described. If the evolution of xi is parameterized by xi(r, z)=(1+z)(-(3+epsilon))(xi(r, 0), where xi(r, 0)=(r/r(0))(-gamma), then epsilon(rho rho) ranges from 1.04+/-0.09 for (1, 0) and 0.18+/-0.12 for (0.2, 0), as measured by the evolution of xi(rho rho) at 1 Mpc (from z similar to 5 to the present epoch). For halos, epsilon depends indeed on their mean overdensity. Halos with a mean overdensity of similar to 2000 were used to compute the halo two-point correlation function, xi(hh), 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 xi(hh) will give a good estimate of the evolution of the galaxy two-point correlation function, at least from z similar to 1 to the present epoch. The values we get for epsilon(hh) range from 1.54 for (1, 0) to -0.36 for (0.2, 0), as measured by the evolution of xi(hh) from z similar to 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, sigma(r, z)(2) similar to GQ rho(z)r(2) xi(r, z), or sigma proportional to (1 + 2)(-epsilon/2). The values of epsilon measured from our simulated velocities differ from those given by the evolution of xi and the CVT, keeping gamma and Q constant: epsilon = 1.78 +/- 0.13 for (1, 0) or epsilon = 1.40 +/-0.28 for (0.2, 0).