Numerical stochastic inflation constrained by frozen noise

TL;DR

This paper introduces a fast, semi-analytical method for computing primordial black hole seed perturbations in single-field inflation models, significantly speeding up previous approaches by treating short-wavelength modes beyond the de Sitter approximation.

Contribution

It develops 'constrained stochastic inflation,' a new efficient approach to calculate inflationary perturbations, including non-Gaussian tails, with a speed-up of a factor of 10^9 over prior methods.

Findings

Perturbation distribution computed in seconds, including non-Gaussian tails.

Method reduces problem to one dimension using mode squeezing and freezing.

Speed-up enables detailed analysis of primordial black hole formation.

Abstract

Stochastic inflation can resolve strong inflationary perturbations, which seed primordial black holes. I present a fast and accurate way to compute these perturbations in typical black hole producing single-field models, treating the short-wavelength Fourier modes beyond the de Sitter approximation. The squeezing and freezing of the modes reduces the problem to one dimension, and the resulting new form of the stochastic equations, dubbed `constrained stochastic inflation,' can be solved efficiently with semi-analytical techniques and numerical importance sampling. In an example case, the perturbation distribution is resolved in seconds deep into its non-Gaussian tail, a speed-up of factor $10^9$ compared to a previous study. Along the way, I comment on the role of the momentum constraint in stochastic inflation.