  High-resolution N-body simulations are used to examine the power spectrum
dependence of the concentration of galaxy-sized dark matter halos. It is found
that dark halo concentrations depend on the amplitude of mass fluctuations as
well as on the ratio of power between small and virial mass scales. This
finding is consistent with the original results of Navarro, Frenk & White
(NFW), and allows their model to be extended to include power spectra
substantially different from Cold Dark Matter (CDM). In particular, the
single-parameter model presented here fits the concentration dependence on halo
mass for truncated power spectra, such as those expected in the warm dark
matter scenario, and predicts a stronger redshift dependence for the
concentration of CDM halos than proposed by NFW. The latter conclusion confirms
recent suggestions by Bullock et al., although this new modeling differs from
theirs in detail. These findings imply that observational limits on the
concentration, such as those provided by estimates of the dark matter content
within individual galaxies, may be used to constrain the amplitude of mass
fluctuations on galactic and subgalactic scales. The constraints on
$\Lambda$CDM models posed by the dark mass within the solar circle in the Milky
Way and by the zero-point of the Tully-Fisher relation are revisited, with the
result that neither dataset is clearly incompatible with the `concordance'
($\Omega_0=0.3$, $\Lambda_0=0.7$, $\sigma_8=0.9$) $\Lambda$CDM cosmogony. This
conclusion differs from that reached recently by Navarro & Steinmetz, a
disagreement that can be traced to inconsistencies in the normalization of the
$\Lambda$CDM power spectrum used in that work.
