Primordial Black Holes and Gravitational Waves in Hybrid Inflation with Chaotic Potentials

Abstract

We study the formation of primordial black hole (PBH) dark matter and the generation of scalar induced secondary gravitational waves (SIGWs) in a non-supersymmetric model of hybrid inflation with chaotic (polynomial-like) potential, including one-loop radiative corrections. A radiatively corrected version of these models is entirely consistent with Planck's data. By adding non-canonical kinetic energy term in the lagrangian, the inflaton experiences a period of ultra-slow-roll, and the amplitude of primordial power spectrum is enhanced to $O(10^{-2})$. The enhanced power spectra of primordial curvature perturbations can have both sharp and broad peaks. %In the enhancement mechanism we explore two possible extensions by employing a Guassian and a step size kinetic function. A wide mass range of PBHs is realized in our model with the frequencies of scalar induced gravitational waves ranged from nHz to kHz. We present several benchmark points where the PBH mass generated during inflation is around $(1 - 100) \, M_{\odot}$, $(10^{-9} - 10^{-7}) \, M_{\odot}$ and $(10^{-16} - 10^{-11}) \, M_{\odot}$. The PBHs can make up most of the dark matter with masses around $(10^{-16} - 10^{-11}) \, M_{\odot}$ and $(1 - 100) \, M_{\odot}$, and their associated SIGWs can be probed by the upcoming ground and space-based gravitational wave (GW) observatories. The evidence of stochastic process recently reported by NANOGrav may be interpreted as SIGWs associated with the formation of PBHs. These SIGWs may also be tested by future interferometer-type GW observations of SKA, DECIGO, LISA, BBO, TaiJi, TianQin, CE and ET.