Constraining changes in the merger history of (P)BH binaries with the stochastic gravitational wave background

TL;DR

This paper demonstrates how current and future gravitational wave background measurements can constrain the merger history and primordial black hole abundance, revealing differences in the stochastic background shape at various frequencies.

Contribution

It introduces a phenomenological model linking merger rate slopes to stochastic background constraints, and discusses how these bounds complement direct merger rate observations.

Findings

Current LIGO/Virgo data constrains high-redshift merger rate slopes.

Steep merger rates alter the stochastic background shape at intermediate frequencies.

Future detectors can break degeneracies in merger history models.

Abstract

Black holes binaries coming from a distribution of primordial black holes might exhibit a large merger rate up to large redshifts. Using a phenomenological model for the merger rate, we show that changes in its slope, up to redshifts $z\sim 4$, are constrained by current limits on the amplitude of the stochastic gravitational wave background from LIGO/Virgo O3 run. This shows that the stochastic background constrains the merger rate for redshifts larger than the single event horizon of detection ($z\simeq 1$ for the same detector). Moreover, we show that for steep merger rates the shape of the stochastic gravitational wave signal at intermediate frequencies differs from the usual $2/3$ IR scaling. We discuss the implications of our model for future experiments in a wide range of frequencies, as the design LIGO/Virgo array, Einstein Telescope, LISA and PTA. Additionally, we show that i) the stochastic background and the present merger rate provide equally constraining bounds on the abundance of PBHs arising from a Gaussian distribution of inhomogeneities and ii) Degeneracies at the level of the stochastic background (i.e. different merger histories leading to a similar stochastic background) can be broken by considering the complementary direct observation of the merger rate from number counts by future detectors such as the Einstein Telescope.