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; δ(t) ∼ 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 sublunar 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.