  We show that a universe dominated by cold dark matter fails to reproduce the
rotation curves of dark matter dominated galaxies, one of the key problems that
it was designed to resolve. We perform numerical simulations of the formation
of dark matter halos, each containing \gsim 10^6 particles and resolved to
0.003 times the virial radius, allowing an accurate comparison with rotation
curve data. A good fit to both galactic and cluster sized halos can be achieved
using the density profile rho(r) \propto [(r/r_s)^1.5(1+(r/r_s)^1.5)]^-1, where
r_s is a scale radius. This profile has a steeper asymptotic slope, rho(r)
\propto r^-1.5, and a sharper turnover than found by lower resolution studies.
The central structure of relaxed halos that form within a hierarchical universe
has a remarkably small scatter (unrelaxed halos would not host disks). We
compare the results with a sample of dark matter dominated, low surface
brightness (LSB) galaxies with circular velocities in the range 100-300 km/s.
The rotation curves of disks within cold dark matter halos rise too steeply to
match these data which require a constant mass density in the central regions.
The same conclusion is reached if we compare the scale free shape of observed
rotation curves with the simulation data. It is important to confirm these
results using stellar rather than HI rotation curves for LSB galaxies. We test
the effects of introducing a cut-off in the power spectrum that may occur in a
universe dominated by warm dark matter. In this case halos form by a monolithic
collapse but the final density profile hardly changes, demonstrating that the
merger history does not play a role in determining the halo structure.
