Stochastic constant-roll inflation and primordial black holes

TL;DR

This paper develops an analytical approach to stochastic constant-roll inflation, showing how stochastic effects influence primordial black hole formation by modifying the required curvature power spectrum, with implications for asteroid-mass black holes.

Contribution

It provides a novel analytical solution for the stochastic constant-roll inflation system using a numerically derived power spectrum, extending beyond the de Sitter approximation.

Findings

Stochastic effects can lower the curvature power spectrum threshold for black hole formation.

The probability distribution depends analytically on the integrated curvature spectrum and slow-roll parameter.

Results are compared with non-stochastic $ abla N$ formalism studies.

Abstract

Stochastic inflation resolves primordial perturbations non-linearly, 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 $\sigma_k^2$ and the second slow-roll parameter $\epsilon_2$. With a large $\epsilon_2$, stochastic effects can reduce the height of the curvature power spectrum required to form asteroid mass black holes from $10^{-2}$ to $10^{-3}$. I compare these results to studies with the non-stochastic $\Delta N$ formalism.