Do Distinct Cosmological Models Predict Degenerate Halo Populations?

Using cosmological N-body simulations, we investigate the influence of the matter density parameter Ω_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 ξ(r), and pairwise velocity statistics v₁₂(r) and σ₁₂(r). For fixed linear theory P(k), the effect of changing Ω_m is simple: the halo mass scale M_* shifts in proportion to Ω_m, pairwise velocities (at fixed M/M_*) are proportional to Ω, and halo clustering at fixed M/M_* is unchanged. If one simultaneously changes the power spectrum amplitude σ₈ to maintain the "cluster normalization" condition σ₈Ω = const, then n(M) stays approximately constant near M ~ 5 × 10¹⁴ 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 Ω_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 spectral tilt n_s or shape parameter Γ, but the required changes are substantial—e.g., masking a decrease of Ω_m from 0.3 to 0.2 requires Δn_s ≈ 0.3 or ΔΓ ≈ 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 Ω_m alone would be detected by any dynamically sensitive clustering statistic; a cluster normalized change to σ₈ and Ω_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.