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

TL;DR

This paper explores how small primordial black holes could serve as dark matter, examining their production during inflation, their gravitational wave signatures, and the implications for future high-frequency GW detection.

Contribution

It introduces a model linking polynomial inflation with non-minimal gravity coupling to PBH dark matter and develops numerical methods to analyze associated gravitational wave signals.

Findings

Small PBHs in the 10^6-10^9 g range can be viable dark matter candidates.

Future GW detectors may observe signals from these PBHs, especially in the high-frequency range.

Standard power spectrum models may need inflationary input for accurate GW signal predictions.

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.