Induced Gravitational Waves probing Primordial Black Hole Dark Matter with Memory Burden

TL;DR

This paper explores how gravitational wave signals induced by primordial curvature perturbations can reveal the presence of primordial black hole dark matter, especially considering the memory burden effect that extends black hole lifetimes.

Contribution

It introduces a novel analysis of induced gravitational waves as probes for primordial black hole dark matter, incorporating the memory burden effect on black hole evaporation.

Findings

Induced GWs peak at specific frequencies depending on PBH mass.

Future detectors like Cosmic Explorer can test PBHs heavier than 10^7 grams.

Detection of high-frequency GWs from PBH mergers can confirm the scenario.

Abstract

Quantum evaporation of a black hole is conventionally studied semiclassically by assuming self-similarity of the black hole throughout the evaporation process. However, its validity was recently questioned, and the lifetime of a black hole is conjectured to be much extended by the memory burden effect. It gives rise to the possibility that the primordial black holes (PBHs) lighter than $10^{10}$ grams are the dark matter in the Universe. To probe such PBH dark matter, we study gravitational waves (GWs) induced by primordial curvature perturbations that produced the PBHs. We find $\Omega_\text{GW}(f_\text{peak})h^2 = 7 \times 10^{-9}$ with the peak frequency $f_\text{peak} = 1\times 10^{3} \, (M_\text{PBH}/(10^{10}\,\mathrm{g}))^{-1/2}\, \mathrm{Hz}$, and the induced GWs associated with the PBH dark matter whose initial mass is greater than about $10^7$ grams can be tested by future observations such as Cosmic Explorer. Furthermore, the scenario can be in principle confirmed by detecting another GW signal from the mergers of PBHs, which leads to high-frequency GWs with $f_\text{peak} = 2 \times 10^{27}\, (M_\text{PBH, ini}/(10^{10}\, \mathrm{g}))^{-1} \, \mathrm{Hz} $. On the other hand, the induced GW signals stronger than expected would contradict the dark matter abundance and exclude the memory burden effect.