Enhanced spectrum of primordial perturbations, galaxy formation and
  small scale structure
  The standard structure formation scenario is successful on linear scales.
Several apparent problems affect it however at galactic scales, such as the
small scale problems at low redshift and more recent issues involving early
massive galaxy and black hole formation. As these problems arise where complex
baryonic physics becomes important, the associated unknowns are often assumed
to be behind the problems. But the same scales are also those where the
primordial spectrum is relatively unconstrained, and there are several ways in
which it can be modified. We focus on that arising from effects possibly
associated with the crossing of high energy cutoff scale by fluctuation modes
during inflation. Elementary arguments show that adiabatic evolution cannot
modify the near scale invariance, we thus discuss a simple model for the
contrary extreme of sudden transition. Numerical calculations and simple
arguments suggest that its predictions, for parameters considered here, are
more generic than may be expected, with significant modifications requiring a
rapid transition. We examine the implications of such a scenario, in this
simplest form of sudden jump, on the matter power spectrum and halo mass
function in light of the limitations imposed by particle production. We show
that enhancement and oscillation in the power spectrum on currently nonlinear
scales can potentially simultaneously alleviate both the apparent problem of
early structure formation and, somewhat counterintuitively, problems at low
redshift such as the apparent dearth of dwarf galaxies. We discuss consequences
that can observationally constrain the scenario and its parameters, including
an inflationary Hubble scale $\lesssim 10^{-8} M_{\rm Pl}$, while touching on
the possibility of simultaneous modification of power on the largest scales.
