Inflation, cold dark matter, and the central density problem

The lingering problem with high central densities in dark halos has arisen in the context of (L)CDM cosmologies with n=1 scale-invariant initial power spectra. Although n=1 is often justified by appealing to the inflation scenario, the choice is not generally justified. Specifically, inflation models with mild but important deviations from scale invariance (nsimilar to0.9) are not uncommon, and those with significant running of the spectral index are quite plausible. Even a mild deviation from scale invariance can be important because halo collapse times and densities depend on the relative amount of small-scale power. Here, we choose several popular, often well-motivated, models of inflation and work out the ramifications for galaxy central densities. For each model, we calculate its COBE-normalized primordial power spectrum and deduce the implied halo densities using a semianalytic method calibrated against N-body simulations. We compare our predictions to a sample of similar to50 dark matter-dominated galaxies using a nonparametric measure of the density, Delta(V/2), defined as the mean mass density, relative to the critical density, within the radius at which the rotation curve falls to half of its maximum value. While standard n=1 LCDM halos are overdense by a factor of similar to6, several of our example inflation+CDM models predict halo densities well within, and even below, the range preferred by observations. We also show how the presence of massive (m(nu)similar to0.5 eV) neutrinos can help to alleviate the central density problem, even with a scale-invariant spectrum. We conclude that galaxy central densities may not be as problematic for the CDM paradigm as is sometimes assumed: rather than telling us something about the nature of dark matter, galaxy rotation curves may be telling us something about inflation and/or neutrinos. An important test of this idea will be an eventual consensus on the value of sigma(8), the rms overdensity on the scale 8h(-1)Mpc. Our successful models tend to have values of sigma(8)approximate to0.75, which is well within the range of recent determinations. Finally, models with n>1 (or sigma(8)greater than or similar to1) are highly disfavored.