A Faster Growth of Perturbations in an Early Matter Dominated Epoch:
  Primordial Black Holes and Gravitational Waves
  We present a scenario for fast growth of cosmological perturbations;
$\delta(t) \sim a(t)^s$, $a(t)$ being the scale factor, with $s > 10$ for the
numerical examples reported in this article. The basic ingredients of the
scenario are an early matter dominated era and the dark fermion which
experiences a scalar mediated force during the epoch. Both of these arise in
string/supergravity models. The fast growth occurs for sub-horizon density
perturbations of the dark fermion. The fast growth has a rich set of
phenomenological implications. We outline implications for the formation of
primordial black holes and the production of gravitational waves. Primordial
black holes in the sub-lunar mass range (which are ideal dark matter
candidates) can be produced. Gravitational waves can be produced in a wide
range of frequencies due to second order scalar perturbations and due to
evaporation and merger of primordial black holes.
