Inflationary relics from an Ultra-Slow-Roll plateau

Abstract

We investigate the formation of primordial black holes (PBHs) in inflationary scenarios featuring an ultra-slow-roll (USR) plateau with a sharp transition to slow roll. We focus on two coexisting production channels: PBHs originating from relic vacuum bubbles where the inflaton got trapped on the plateau, and PBHs arising from standard adiabatic density perturbations. From detailed numerical simulations we find that the bubbles are generically surrounded by type-II curvature fluctuations. Special attention is given to the distribution of initial conditions, including the relevant mean profiles and shape dispersion around them. For the adiabatic channel, we extend the logarithmic template formula $\zeta[\zeta_G]$, which maps the Gaussian curvature perturbation to the fully non-Gaussian one while incorporating mode evolution, and we compare this with numerical results obtained using the $\delta N$ formalism. While the template departs from numerical results near its logarithmic divergence, it still provides accurate threshold values for PBH formation in the parameter range relevant to our analysis. Finally, we compute the PBH mass functions for both channels. We find that the adiabatic channel dominates over the bubble-induced channel by a factor $\sim \mathcal{O}(10-10^{2})$, and that both contributions are largely dominated by the mean profiles.