We investigate the enhancement of the curvature perturbations in a single-field slow-roll inflation with a spectator scalar field kinetically coupled to the inflaton. The coupling term with a periodic function of inflaton triggers the exponential growth of the spectator field perturbations, which indirectly amplifies the curvature perturbations to produce a sizable abundance of primordial black holes (PBHs). This scenario is found to be insensitive to the inflationary background. We study two distinct populations of the stochastic gravitational wave background (SGWB) produced in this scenario, i.e., induced by the scalar perturbations during the inflationary era and the radiation-dominated era, respectively. With the appropriate choices of parameter space, we consider two PBH mass windows of great interest. One is PBHs of masses $\mathcal{O}({10}^{-12})M_{\odot }$ that can be a vital component of dark matter, and the predicted total energy spectrum of SGWB shows a unique profile and is detectable by LISA and Taiji. The other is PBHs of masses $\mathcal{O}(10)M_{\odot }$ which can provide consistent explanation for the LIGO-Virgo events. More interestingly, the predicted gravitational wave signal from the radiation-dominated era may account for the NANOGrav 12.5-yr results.

• Received 12 August 2021
• Accepted 20 September 2021

DOI:https://doi.org/10.1103/PhysRevD.104.083537