Do Distinct Cosmological Models Predict Degenerate Halo Populations?

Using cosmological N-body simulations, we investigate the influence of the matter density parameter Omega_m 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 Omega_m is simple: the halo mass scale M_* shifts in proportion to Omega_m, pairwise velocities (at fixed M/M_*) are proportional to Omega_m^{0.6}, and halo clustering at fixed M/M_* is unchanged. If one simultaneously changes the P(k) amplitude sigma_8 to maintain a "cluster normalization" condition sigma_8 x Omega_m^{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 Omega_m 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 Omega_m alone would be detected by any dynamically sensitive clustering statistic; a cluster normalized change to sigma_8 and Omega_m 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.