A Faster Growth of Perturbations in an Early Matter Dominated Epoch: Primordial Black Holes and Gravitational Waves

Abstract

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.

Typos corrected, new numerical examples provided, references added

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