Boosted perturbations at the end of inflation
  We study the effect on the primordial cosmological perturbations of a sharp
transition from inflationary to a radiation and matter dominated epoch
respectively. We assume that the perturbations are generated by the vacuum
fluctuations of a scalar field slowly rolling down its potential, and that the
transition into the subsequent epoch takes place much faster than a Hubble
time. The behaviour of the superhorizon perturbations corresponding to
cosmological scales in this case is well known. However, it is not clear how
perturbations on scales of and smaller than the Hubble horizon scale at the end
of inflation may evolve through such a transition. We derive the evolution
equation for the gravitational potential $\Psi$, which allows us to study the
evolution of the perturbations on all scales under these circumstances. We show
that for a certain range of scales inside the horizon at the end of inflation,
the amplitude of the perturbations are enhanced relative to the superhorizon
scales. This enhancement may lead to the overproduction of Primordial Black
Holes (PBHs), and therefore constrain the dynamics of the transitions that take
place at the end of inflation.
