Primordial black holes and induced gravitational waves from localized features in DBI inflation
We investigate primordial black hole formation in a Dirac-Born-Infeld inflationary framework in which the background dynamics are determined by explicit functional forms of the inflaton potential $V(\phi)$ and the warp factor $f(\phi)$. The background equations are solved numerically to obtain the evolution of the slow-roll parameters. We show that a localized feature in the potential, accompanied by a correlated structure in the warp factor, dynamically induces a transient suppression of the slow-roll parameter, leading to a short-lived non-attractor phase. This behavior generates an enhancement of the curvature power spectrum on small scales, while preserving consistency with CMB-scale observables. The Mukhanov-Sasaki equation is then solved numerically to compute the resulting power spectrum, which exhibits narrow and localized peaks in the PBH abundance across different mass ranges. We also evaluate the associated stochastic background of induced gravitational waves and find that the predicted signal can fall within the sensitivity bands of future pulsar timing arrays and space-based interferometers, depending on the scale of the inflationary feature. A parameter scan in the $(r,n_s)$ plane shows that the large-scale predictions remain consistent with current observational constraints.