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

Abstract

A perturbation on the background inflaton potential can lead inflation into the ultraslow-roll stage and can thus remarkably enhance the power spectrum ${\mathcal{P}}_{\mathcal{R}}(k)$ of the primordial curvature perturbation on small scales. Such an enhanced ${\mathcal{P}}_{\mathcal{R}}(k)$ 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 $f_{\mathrm{PBH}}(M)$ and SIGW spectra ${\Omega }_{\mathrm{GW}}(f)$ 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 $30M_{\odot }$, 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 $30M_{\odot }$ can also interpret the potential isotropic stochastic gravitational wave background from the NANOGrav 12.5-year dataset.

arXiv comment22 pages, 6 figures

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