Stochastic constant-roll inflation and primordial black holes
Eemeli Tomberg
Abstract
Stochastic inflation resolves primordial perturbations nonlinearly, probing their probability distribution deep into its non-Gaussian tail. The strongest perturbations collapse into primordial black holes. In typical black-hole-producing single-field inflation, the strongest stochastic kicks occur during a period of constant roll. In this paper, I solve the stochastic constant-roll system, drawing the stochastic kicks from a numerically computed power spectrum, beyond the usual de Sitter approximation. The perturbation probability distribution is an analytical function of the integrated curvature power spectrum ${\ensuremath{\sigma}}_{k}^{2}$ and the second slow-roll parameter ${\ensuremath{\epsilon}}_{2}$. With a large ${\ensuremath{\epsilon}}_{2}$, stochastic effects can reduce the height of the curvature power spectrum required to form asteroid mass black holes from ${10}^{\ensuremath{-}2}$ to ${10}^{\ensuremath{-}3}$. I compare these results to studies with the nonstochastic $\mathrm{\ensuremath{\Delta}}N$ formalism.