![[OSU Physics logo]](/Images/osu-physics.gif)
In the standard, LCDM model of cosmology, the Universe is dominated by collisionless, cold dark matter (CDM) and a cosmological constant ($\Lambda$). According to this model, structure formed hierarchically via the growth of Gaussian density fluctuations generated during an inflationary epoch in the very early Universe. The standard assumption is that the primordial power spectrum of density fluctuations took on the scale-invariant, Harrison-Zel'dovich form (\ie, $P(k) \propto k^n$ with $n=1.0$). While this standard model can account for an impressive range of large-scale observations, it has difficulties explaining observations on galactic and sub-galactic scales.
I will begin with an overview of the standard model of structure formation and a brief discussion of a semi-analytic model that can be used to predict the central densities of CDM halos. I will then describe the {\em central density problem}: LCDM with $n=1.0$ predicts dark halos that are overdense by a factor of $\sim 8$ compared to the densities inferred from observed galaxy rotation curves. I will propose two possible resolutions to the central density problem that do not require a modification of the CDM properties. First, generic models of inflation do not predict primordial power spectra that are {\em exactly} scale-invariant. I will show that by accounting for the small, but important, deviations from $n=1.0$ and the scale-dependence of the effective spectral index predicted by broad classes of inflationary models, the central density problem can be alleviated or even eliminated. Second, massive neutrinos tend to damp power on small scales due to ``free-streaming.'' I will show that a neutrino mass of $m_{\nu} \sim 0.5$ eV can also eliminate the central density problem. My conclusion is that galaxy rotation curves may be teaching us about inflation and/or neutrinos as well as the properties of CDM.
