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 (n~0.9) 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 ~50 dark matter-dominated galaxies using a nonparametric measure of the density, ΔV/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 ~6, 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_ν~0.5 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 σ₈, the rms overdensity on the scale 8h^-1Mpc. Our successful models tend to have values of σ₈≈0.75, which is well within the range of recent determinations. Finally, models with $n>1$ (or σ₈1) are highly disfavored.