Gravitational waves induced from primordial black hole fluctuations: The effect of an extended mass function

TL;DR

This paper investigates the gravitational wave background generated by primordial black holes with an extended mass distribution, considering a realistic primordial power spectrum, and finds conditions under which the signal could be detected by LISA.

Contribution

It extends previous models by analyzing the stochastic gravitational-wave background from PBHs with a realistic mass function derived from a power-law primordial spectrum.

Findings

The GW signal depends on the running spectral index within a narrow range.

An early PBH-dominated era can be triggered without conflicting with BBN constraints.

The predicted GW signal could be detectable by LISA.

Abstract

The gravitational potential of initially Poisson distributed primordial black holes (PBH) can induce a stochastic gravitational-wave background (SGWB) at second order in cosmological perturbation theory. This SGWB was previously studied in the context of general relativity (GR) and modified gravity setups by assuming a monochromatic PBH mass function. Here we extend the previous analysis in the context of GR by studying the aforementioned SGWB within more physically realistic regimes where PBHs have different masses. In particular, starting from a power-law cosmologically motivated primordial curvature power spectrum with a running spectral index we extract the extended PBH mass function and the associated to it PBH gravitational potential which acts as the source of the scalar induced SGWB. At the end, by taking into account the dynamical evolution of the PBH gravitational potential during the transition from the matter era driven by PBHs to the radiation era we extract the respective GW signal today. Interestingly, in order to trigger an early PBH-dominated era and avoid the GW constraints at BBN we find that the running of the spectral index $\alpha_\mathrm{s}$ of our primordial curvature power spectrum should be within the narrow range $\alpha_\mathrm{s}\in[3.316,3.355]\times 10^{-3}$ while at the same time the GW signal is found to be potentially detectable by LISA.