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 ${\cal P}_{\cal R}(k)$ 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.