Inflationary and Gravitational Wave Signatures of Small Primordial Black Holes as Dark Matter

Abstract: Mounting evidence suggests that the semi-classical description of a black hole breaks down at the latest after losing an O(1) fraction of its mass. As a result, effects such as memory burden can slow down evaporation so that small primordial black holes (PBHs), in particular those in the mass range 10^6 g to 10^9 g, become viable dark matter candidates. In this paper, we investigate the production of PBHs from a prototype model of polynomial inflation with a non-minimal coupling to gravity. We show that a sufficiently small PBH mass alleviates any tension with CMB observations. Moreover, we develop efficient numerical procedures to identify model parameters and evolve Mukhanov-Sasaki modes to place bounds on the scalar-induced stochastic gravitational wave (GW) background. Whilst we identify some prospects for observation with future GW detectors, our results highlight the need to develop new experiments for high-frequency GW detection in the ~kHz to ~MHz range. Finally, we demonstrate that previously-used ans\"atze for modelling the power spectrum only yield a reliable approximation for the GW signal if some input from inflation is used.