  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 ~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 ~ 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 ~0.85 predict a factor
of ~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_sub
> 0.01 even for an effective tilt of n ~0.8.We conclude that, at their current
level, lensing constraints of this kind do not provide strong limits on the
primordial power spectrum.
