Do Distinct Cosmological Models Predict Degenerate Halo Populations?

Using cosmological N-body simulations, we investigate the influence of the matter density parameter Omegaₘ and the linear theory power spectrum P (k) on statistical properties of the dark matter halo population -- the mass function n (M), the halo correlation function, and halo pairwise velocity statistics. For fixed P (k), the effect of changing Omegaₘ is simple: the halo mass scale M_* shifts in proportion to Omegaₘ, pairwise velocities (at fixed M/M_*) are proportional to Omegaₘ^0. 6, and halo clustering at fixed M/M_* is unchanged. If one simultaneously changes the P (k) amplitude sigma₈ to maintain a "cluster normalization" condition sigma₈ x Omegaₘ^0. 5 = const, then n (M) stays approximately constant near M ~ 5e14 Msun, and halo clustering and pairwise velocities are similar at fixed M. However, the shape of n (M) changes, with a decrease of Omegaₘ from 0. 3 to 0. 2 producing a ~30% drop in the number of low mass halos. One can preserve the shape of n (M) over a large dynamic range by changing the shape of P (k), but the required changes are substantial, and they significantly alter the halo clustering and halo velocities. The sensitivity of the dark halo population to cosmological model parameters has encouraging implications for efforts to constrain cosmology and galaxy bias with observed galaxy clustering, since the predicted changes in the halo population cannot easily be masked by altering the way that galaxies occupy halos. A shift in Omegaₘ alone would be detected by any dynamically sensitive clustering statistic; a cluster normalized change to sigma₈ and Omegaₘ would require a change in galaxy occupation as a function of M/M_*, which would alter galaxy clustering; and a simultaneous change to P (k) that preserves the halo mass function would change the clustering of the halos themselves.