Numerical simulations of stochastic inflation using importance sampling

TL;DR

This paper introduces a new importance sampling method and software package, PyFPT, for efficiently simulating rare fluctuations in stochastic inflation, enabling detailed statistical analysis of inflationary models.

Contribution

The authors develop and validate a novel importance sampling approach with a publicly available tool for solving first-passage time problems in stochastic inflation, improving computational efficiency.

Findings

Accurate reconstruction of rare fluctuation statistics in quadratic inflation.

Efficient computation reaching probabilities of less than one Hubble patch per universe.

Large-field boundaries can significantly influence the tail of the probability distribution.

Abstract

We show how importance sampling can be used to reconstruct the statistics of rare cosmological fluctuations in stochastic inflation. We have developed a publicly available package, PyFPT, that solves the first-passage time problem of generic one-dimensional Langevin processes. In the stochastic-$\delta N$ formalism, these are related to the curvature perturbation at the end of inflation. We apply this method to quadratic inflation, where the existence of semi-analytical results allows us to benchmark our approach. We find excellent agreement within the estimated statistical error, both in the drift- and diffusion-dominated regimes. The computation takes at most a few hours on a single CPU, and can reach probability values corresponding to less than one Hubble patch per observable universe at the end of inflation. With direct sampling, this would take more than the age of the universe to simulate even with the best current supercomputers. As an application, we study how the presence of large-field boundaries might affect the tail of the probability distribution. We also find that non-perturbative deviations from Gaussianity are not always of the simple exponential type.