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 v _ { 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 \sigma _ { 8 } to maintain the “ cluster normalization ” condition \sigma _ { 8 } \Omega _ { m } ^ { 0.5 } = const , then n ( M ) stays approximately constant near M \sim 5 \times 10 ^ { 14 } h ^ { -1 } M _ { \odot } , 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 \sim 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 \Gamma , but the required changes are substantial — e.g. , masking a decrease of \Omega _ { m } from 0.3 to 0.2 requires \Delta n _ { s } \approx 0.3 or \Delta \Gamma \approx 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 can not 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 .