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

TL;DR

This work investigates gravitational wave signatures associated with PBH dark matter formed from inflationary curvature perturbations. It compares Gaussian and non-Gaussian ($\chi^2$) statistics for the primordial perturbations and analyzes how accretion/merging shapes the PBH mass function and the resulting SGWB. It finds that non-Gaussian rolling-axion scenarios are GW-dominated by primordial signals, while Gaussian models can have a sizable induced GW component; the SGWB spectrum, its peak frequency via $f_{\rm peak} \propto M_{\rm f}^{-1/2}$, and potential $\mu$-distortions offer complementary probes when combined with PTA/LISA data and PIXIE, enabling constraints on inflationary mechanisms for PBH production. The results emphasize that future observations by PTA-SKA and LISA can reveal the inflationary origin of PBH and track PBH evolution through accretion and mergers, providing a window into small-scale physics beyond CMB/LSS.

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 $χ^2$) 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 $μ$-distortions. Therefore the above results can be complemented by the detection (or the absence) of $μ$-distortions with an experiment such as PIXIE.

Figures (12)

• Figure 1: Limits on the present dark matter fraction in PBH, $f_{\rm PBH}$ (left panel), and on the fraction $\beta$ of regions that collapse to form a black hole (right panel). See the text for details.
• Figure 2: PBH limits on the power spectrum of the primordial scalar perturbations, assuming that the perturbations obey a Gaussian (solid line) vs. a $\chi^2$ (dashed line) statistics. The limits are obtained from the right panel of Figure \ref{['fig:limits']}, using Eqs. (\ref{['gauss-chi2']}). We note that the power spectrum is much more constrained in the case of a $\chi^2$ statistics, as the perturbations in the tail of the distribution lead to a greater amount of PBH with respect to the Gaussian case.
• Figure 3: Diagrammatic expression for the GW induced by scalar perturbations in the Gaussian bump model.
• Figure 4: Primordial and induced GW in the rolling axion bump model.
• Figure 5: One and two-loop contributions to the GW signal in the rolling axion bump model. These diagrams give the amplitude of the primordial GW, and of the cross-correlation with the induced GW. Intermediate solid (resp. wiggly) lines represent scalar (resp. gauge field) perturbations.