Unveiling Primordial Black Hole Relics Through Induced Gravitational Waves

TL;DR

This paper explores how induced gravitational waves can reveal the existence and properties of primordial black hole relics, potentially accounting for dark matter, and discusses their detectability with future gravitational wave detectors.

Contribution

It introduces a method to infer primordial black hole relics and their abundance from gravitational wave signals, linking relic properties to observable gravitational wave peaks.

Findings

Peak frequency of gravitational waves scales as the cube root of relic fraction.

Predicted gravitational wave amplitudes could be detectable by upcoming experiments.

Number density of relics can be inferred from gravitational wave peak positions.

Abstract

Black hole relics are of significant interest in cosmology and theoretical physics. In this work, we consider tiny primordial black holes (PBHs) ( $M_{\text {PBH }} \lesssim 10^7 \mathrm{~g}$ ) which are generated soon after the end of inflation and evaporate and reheat the Universe before big bang nucleosynthesis (BBN), but leave their remnants due to incomplete evaporation. These PBHs remnants may contribute as part or all of the dark matter (DM) today. Assuming that there exist PBH relics, we point out that the number density of PBH today can be directly read from the peak positions of the induced gravitational waves due to the inhomogeneous PBH distribution. If PBH relics are of Planck mass and they forms all the DM today, the PBH number density would be of $10^{-25} \mathrm{~cm}^{-3}$ with the peak frequency 60 Hz . The peak frequency scales as $f_{\text {relic }}^{1 / 3}$ where $f_{\text {relic }}$ is the fraction of the PBH relics in the total DM density. The peak amplitude carries the information of initial PBH abundance. For monochromatic-mass PBH with the current number density $10^{-41} \sim 10^{-25} \mathrm{~cm}^{-3}$ and initial abundance $10^{-13} \sim 10^{-7}$, the amplitude may be large enough to be detected by planned gravitational wave experiments in the near future.