Primordial black holes from null energy condition violation during inflation

Abstract: Primordial black holes (PBHs) and the violation of the null energy condition (NEC) have significant implications for our understanding of the very early universe. We present a novel approach to generate PBHs via the NEC violation in a single-field inflationary scenario. In our scenario, the universe transitions from a first slow-roll inflation stage with a Hubble parameter $H = H_{\text{inf}1}$ to a second slow-roll inflation stage with $H = H_{\text{inf}2}\gg H_{\text{inf}1}$, passing through an intermediate stage of NEC violation. The NEC violation naturally enhances the primordial scalar power spectrum at a certain wavelength, leading to the production of PBHs with masses and abundances of observational interest. We also investigate the phenomenological signatures of scalar-induced gravitational waves (SIGWs) resulting from the enhanced density perturbations. Our work highlights the potential of utilizing a combination of PBHs, SIGWs, and primordial gravitational waves as a valuable probe for studying NEC violation during inflation, opening up new avenues for exploring the early universe.