A new algorithm for calculating the curvature perturbations in stochastic inflation

TL;DR

This paper introduces a non-perturbative algorithm within the stochastic inflation framework to compute curvature perturbations, aligning with standard results and enabling numerical analysis of complex inflation models.

Contribution

A novel non-perturbative method for calculating curvature perturbations during inflation using stochastic formalism and the $ abla N$ approach.

Findings

Analytical proof of consistency with standard single-field slow-roll results

Development of an algorithm for numerical calculations in complex inflation models

Automatic inclusion of higher-order perturbation contributions

Abstract

We propose a new approach for calculating the curvature perturbations produced during inflation in the stochastic formalism. In our formalism, the fluctuations of the e-foldings are directly calculated without perturbatively expanding the inflaton field and they are connected to the curvature perturbations by the $\delta N$ formalism. The result automatically includes the contributions of the higher order perturbations because we solve the equation of motion non-perturbatively. In this paper, we analytically prove that our result (the power spectrum and the nonlinearity parameter) is consistent with the standard result in single field slow-roll inflation. We also describe the algorithm for numerical calculations of the curvature perturbations in more general inflation models.