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

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 $f_{\mathrm{P}\mathrm{B}\mathrm{H}}(M)$ and SIGW spectra ${\mathrm{\Omega }}_{\mathrm{G}\mathrm{W}}(f)$ 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.