Primordial black holes and scalar-induced gravitational waves from the perturbations on the inflaton potential in peak theory

TL;DR

This paper investigates how perturbations in the inflaton potential can produce primordial black holes and scalar-induced gravitational waves, with potential observability in future detectors and relevance to the NANOGrav gravitational wave background.

Contribution

It calculates PBH abundances and SIGW spectra using peak theory, identifying mass windows where PBHs could account for dark matter and explaining the NANOGrav signal.

Findings

PBHs in mass windows at 10^{-17} M_sun, 10^{-13} M_sun, and 30 M_sun are achievable.

Generated SIGWs are within the sensitivity of next-generation detectors.

SIGWs related to 30 M_sun PBHs may explain the NANOGrav background.

Abstract

A perturbation on the background inflaton potential can lead inflation into the ultraslow-roll stage and can thus remarkably enhance the power spectrum ${\cal P}_{\cal R}(k)$ of the primordial curvature perturbation on small scales. Such an enhanced ${\cal P}_{\cal R}(k)$ will result in primordial black holes (PBHs), contributing a significant fraction of dark matter, and will simultaneously generate sizable scalar-induced gravitational waves (SIGWs) as a secondorder effect. In this work, we calculate the PBH abundances $f_{\rm PBH}(M)$ and SIGW spectra $\Omega_{\rm GW}(f)$ in peak theory. We obtain the PBHs with desirable abundances in one or two typical mass windows at $10^{-17}\, M_\odot$, $10^{-13}\, M_\odot$, and $30\, M_\odot$, respectively. At the same time, the relevant SIGWs are expected to be observed by the next-generation gravitational wave detectors, without spoiling the current constraint. Especially, the SIGW associated with the PBH of $30\, M_\odot$ can also interpret the potential isotropic stochastic gravitational wave background from the NANOGrav 12.5-year dataset.