# GUT-Scale Primordial Black Holes: Mergers and Gravitational Waves

## TL;DR

This paper investigates the gravitational wave signatures from light primordial black holes that could have dominated the early universe, focusing on classical mergers and their detectability, and assesses how accretion affects black hole lifetimes.

## Contribution

It introduces the analysis of classical mergers of primordial black holes in a matter-dominated phase and evaluates their gravitational wave background, considering effects of accretion on black hole evolution.

## Key findings

- Mergers produce a stochastic gravitational wave background with $\, ext{Ω}_ ext{GW} \, ext{~} 10^{-12}$
- Background frequencies range from $10^{15}$ to $10^{19}$ Hz
- Accretion increases black hole mass by ~14% and lifetime by ~50%

## Abstract

Tight constraints on the abundance of primordial black holes can be deduced across a vast range of masses, with the exception of those light enough to fully evaporate before nucleosynthesis. This hypothetical population is almost entirely unconstrained, to the point where the early Universe could pass through a matter-dominated phase with primordial black holes as the primary component. The only obvious relic of this phase would be Hawking radiated gravitons which would constitute a stochastic gravitational wave background in the present-day Universe, albeit at frequencies far beyond the scope of any planned detector technology. This paper explores the effects of classical mergers in such a matter dominated phase. For certain ranges of parameters, a significant fraction of the black holes merge, providing an additional, classical source of primordial gravitational waves. The resulting stochastic background typically has a lower amplitude than the Hawking background and lies at less extreme frequencies, but is unlikely to be easily detectable, with a maximal present day density of $\Omega_{GW} \sim 10^{-12}$ and frequencies between $10^{15} - 10^{19}$ Hz. We also asses the impact of radiation accretion on the lifetimes of such primordial black holes and find that it increases the black hole mass by $\sim 14 \%$ and the lifetimes by about $50 \%$. However, this does not qualitatively change any of our conclusions.