Primordial Black Hole Mass Function with Mass Gap

TL;DR

This paper models the primordial black hole mass function with a mass gap, analyzes its implications for gravitational wave signals, and suggests that detecting specific features can inform inflationary physics.

Contribution

It introduces a method to incorporate a mass gap into the PBH mass function and explores its effects on gravitational wave background spectra.

Findings

The first peak of the gravitational wave spectrum is independent of the mass gap.

A smaller trough at higher frequencies is predicted due to the mass gap.

Detection of the trough can provide insights into inflation and PBH formation.

Abstract

Primordial black holes (PBHs) are mainly characterized by their mass function, in which there may be some huge suppression for certain mass spans. If this is the case, the absence of these PBHs will form mass gaps. In this paper, we investigate the PBH mass function with mass gap. Firstly, to obtain a data-supported PBH mass function with mass gap for subsolar masses PBHs, we fine-tune the coefficients of a model-independent power spectrum of primordial curvature perturbations. Then we take this unique PBH mass function into consideration and calculate the energy density spectrum of the stochastic gravitational wave background from PBH mergers. We find the location of its first peak almost has no relationship with the mass gap and is only determined by the probability distribution of frequencies at which PBH binaries merge. Apart from the first peak, there must be an accompanying smaller trough at higher frequency resulting from the mass gap. Therefore, the detection of this smaller trough will provide more information about inflation and PBH formation.