Inflationary relics from an Ultra-Slow-Roll plateau

TL;DR

This paper explores primordial black hole formation during inflation with an ultra-slow-roll plateau, analyzing two production channels and extending non-Gaussian perturbation models to predict PBH mass functions.

Contribution

It introduces an extended logarithmic template for non-Gaussian curvature perturbations and compares it with numerical simulations, providing new insights into PBH formation mechanisms.

Findings

Adiabatic channel dominates PBH production over bubble-induced channel by 10 to 100 times.

The extended template accurately predicts PBH formation thresholds despite divergence issues.

Both channels are primarily influenced by the mean profiles of initial conditions.

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.