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), two-point correlation function xi(r), and pairwise velocity statistics nu(12)(r) and sigma(12)(r). For fixed linear theory 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 power spectrum amplitude 8 to maintain the cluster normalization condition sigma(8)Omega(m)(0.5) = const, then n(M) stays approximately constant near M similar to5 x 10(14) h(-1) M-.(,) and halo clustering and pairwise velocities are similar at fixed M. However, the shape of n(M) changes, with a decrease of m from 0.3 to 0.2, producing a similar to30% drop in the number of low-mass halos. One can preserve the shape of n(M) over a large dynamic range by changing the spectral tilt n(s) or shape parameter Gamma, but the required changes are substantial e.g., masking a decrease of Omega(m) from 0.3 to 0.2 requires Deltan(s) approximate to 0.3 or DeltaGamma approximate to 0.15. These changes to P(k) 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 m alone would be detected by any dynamically sensitive clustering statistic; a cluster normalized change to 8 and 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.