Detecting the Stochastic Gravitational Wave Background from Primordial Black Hole Formation

TL;DR

This paper investigates the gravitational wave background generated by primordial black hole formation, analyzing its amplitude and shape across models, and discusses the potential of current and future detectors to observe or constrain PBHs as dark matter candidates.

Contribution

It provides a detailed analysis of the stochastic gravitational wave background from PBH formation across various models and evaluates the detectability with upcoming gravitational wave observatories.

Findings

The gravitational wave background is enhanced for broad or nearly scale-invariant spectra.

Current pulsar timing limits strongly constrain PBHs from Gaussian fluctuations with wide mass distributions.

Future detectors like LISA and SKA can probe PBHs down to very small masses and even detect single stellar-mass PBHs.

Abstract

Primordial Black Holes (PBH) from peaks in the curvature power spectrum could constitute today an important fraction of the Dark Matter in the Universe. At horizon reentry, during the radiation era, order one fluctuations collapse gravitationally to form black holes and, at the same time, generate a stochastic background of gravitational waves coming from second order anisotropic stresses in matter. We study the amplitude and shape of this background for several phenomenological models of the curvature power spectrum that can be embedded in waterfall hybrid inflation, axion, domain wall, and boosts of PBH formation at the QCD transition. For a broad peak or a nearly scale invariant spectrum, this stochastic background is generically enhanced by about one order of magnitude, compared to a sharp feature. As a result, stellar-mass PBH from Gaussian fluctuations with a wide mass distribution are already in strong tension with the limits from Pulsar Timing Arrays, if they constitute a non negligible fraction of the Dark Matter. But this result is mitigated by the uncertainties on the curvature threshold leading to PBH formation. LISA will have the sensitivity to detect or rule out light PBH down to $10^{-14} M_{\odot}$. Upcoming runs of LIGO/Virgo and future interferometers such as the Einstein Telescope will increase the frequency lever arm to constrain PBH from the QCD transition. Ultimately, the future SKA Pulsar Timing Arrays could probe the existence of even a single stellar-mass PBH in our Observable Universe.