Gravitational Wave signatures of inflationary models from Primordial Black Hole Dark Matter

TL;DR

This paper investigates the gravitational wave signatures associated with primordial black hole formation during inflation, analyzing how these signals depend on primordial fluctuation statistics and PBH evolution, and how they can be detected or constrained by current and future experiments.

Contribution

It provides a detailed analysis of the gravitational wave background from PBH formation, considering different fluctuation statistics and PBH evolution scenarios, and compares predictions with detector sensitivities.

Findings

SGWB amplitude and frequency range depend on fluctuation statistics and PBH evolution.

The SGWB can be used to probe or constrain early universe PBH production mechanisms.

Different assumptions lead to varying levels of CMB μ-distortions, testable by experiments like PIXIE.

Abstract

Primordial Black Holes (PBH) could be the cold dark matter of the universe. They could have arisen from large (order one) curvature fluctuations produced during inflation that reentered the horizon in the radiation era. At reentry, these fluctuations source gravitational waves (GW) via second order anisotropic stresses. These GW, together with those (possibly) sourced during inflation by the same mechanism responsible for the large curvature fluctuations, constitute a primordial stochastic GW background (SGWB) that unavoidably accompanies the PBH formation. We study how the amplitude and the range of frequencies of this signal depend on the statistics (Gaussian versus $\chi^2$) of the primordial curvature fluctuations, and on the evolution of the PBH mass function due to accretion and merging. We then compare this signal with the sensitivity of present and future detectors, at PTA and LISA scales. We find that this SGWB will help to probe, or strongly constrain, the early universe mechanism of PBH production. The comparison between the peak mass of the PBH distribution and the peak frequency of this SGWB will provide important information on the merging and accretion evolution of the PBH mass distribution from their formation to the present era. Different assumptions on the statistics and on the PBH evolution also result in different amounts of CMB $\mu$-distortions. Therefore the above results can be complemented by the detection (or the absence) of $\mu$-distortions with an experiment such as PIXIE.