Constraints on the induced gravitational wave background from primordial black holes

TL;DR

This paper calculates the primordial black hole mass spectrum and the associated second-order gravitational wave background, extending constraints across a wider frequency range and analyzing the implications for PBH abundance using pulsar timing data.

Contribution

It provides a consistent calculation of PBH mass spectrum and GW background, showing that maximal GW amplitudes are largely independent of primordial spectrum shape and extending existing constraints.

Findings

Maximal GW amplitudes are insensitive to primordial spectrum shape.

Constraints on GW background are extended to wider frequency ranges.

Pulsar timing limits can strongly constrain PBH abundance in certain mass ranges.

Abstract

We perform a consistent calculation of primordial black hole (PBH) mass spectrum and second-order induced gravitational wave (GW) background produced from primordial scalar perturbations in radiation era of the early Universe. It is shown that the maximal amplitudes of the second order GW spectrum that can be approached without conflicting with the PBH data do not depend significantly on the shape of primordial perturbation spectrum. The constraints on the GW background obtained in previous works are extended to a wider GW frequency range. We discuss the applicability of the currently available pulsar timing limits for obtaining the constraints on scalar power spectrum and PBH abundance and show that they can be used for strongly constraining the PBH number density in the PBH mass range $\sim (0.03 - 10) M_{\odot}$.