Gravitational-Wave Constraints on the Abundance of Primordial Black Holes

TL;DR

This paper explores how gravitational wave signals induced by primordial density fluctuations relate to the abundance of primordial black holes, providing constraints on their properties across a range of masses using current and future detectors.

Contribution

It demonstrates the insensitivity of the GW spectrum to peak width in density fluctuations and establishes a method to constrain primordial black hole abundance from GW observations.

Findings

Primordial black holes with masses 10^{20-26}g can be detected by space-based and atomic interferometers.

GW spectrum amplitude decreases with increasing peak width in density fluctuations.

Constraints on supermassive primordial black holes are derived from CMB observations.

Abstract

We investigate features of Gravitational Waves (GWs) induced by primordial density fluctuations with a large amplitude peak associated with formation of Primordial Black Holes (PBHs). It is shown that the spectrum of induced GW is insensitive to the width of the peak in wavenumber space provided it is below a certain value, but the amplitude of the spectrum reduces at the peak frequency and decreases faster at low frequencies for a larger width. A correspondence between the GW amplitude and PBH abundance is also investigated incorporating the peak width. We find that PBHs with masses 10^{20-26}g can be probed by space-based laser interferometers and atomic interferometers irrespective of whether the peak width is small or not. Further we obtain constraints on the abundance of the supermassive PBHs by comparing a low frequency tail of the GW spectrum with CMB observations.