Although the currently favored cold dark matter plus cosmological constant model for structure formation assumes an n = 1 scale-invariant initial power spectrum , most inflation models produce at least mild deviations from n = 1 .
Because the lever arm from the CMB normalization to galaxy scales is long , even a small “ tilt ” can have important implications for galactic observations .
Here we calculate the COBE-normalized power spectra for several well-motivated models of inflation and compute implications for the substructure content and central densities of galaxy halos .
Using an analytic model , normalized against N-body simulations , we show that while halos in the standard ( n = 1 ) model are overdense by a factor of \sim 6 compared to observations , several of our example inflation+LCDM models predict halo densities well within the range of observations , which prefer models with n \sim 0.85 .
We go on to use a semi-analytic model ( also normalized against N-body simulations ) to follow the merger histories of galaxy-sized halos and track the orbital decay , disruption , and evolution of the merging substructure .
Models with n \sim 0.85 predict a factor of \sim 3 fewer subhalos at a fixed circular velocity than the standard n = 1 case .
Although this level of reduction does not resolve the “ dwarf satellite problem ” , it does imply that the level of feedback required to match the observed number of dwarfs is sensitive to the initial power spectrum .
Finally , the fraction of galaxy-halo mass that is bound up in substructure is consistent with limits imposed by multiply imaged quasars for all models considered : f _ { sat } > 0.01 even for an effective tilt of n \sim 0.8 .
We conclude that , at their current level , lensing constraints of this kind do not provide strong limits on the primordial power spectrum .