Non-perturbative approach for curvature perturbations in stochastic-$\delta N$ formalism

TL;DR

This paper introduces a non-perturbative algorithm within the stochastic-$ abla N$ formalism to accurately compute curvature perturbations in inflation, especially in highly stochastic or non-Gaussian regimes where traditional methods fail.

Contribution

The paper presents a novel non-perturbative computational method for curvature perturbations applicable to complex inflation models, overcoming limitations of perturbative approaches.

Findings

Successfully applied to chaotic inflation model, confirming known results.

Effectively computed curvature perturbations in hybrid inflation near the critical point.

Demonstrated the method's robustness in scenarios with large non-Gaussianities.

Abstract

In our previous paper, we have proposed a new algorithm to calculate the power spectrum of the curvature perturbations generated in inflationary universe with use of the stochastic approach. Since this algorithm does not need the perturbative expansion with respect to the inflaton fields on super-horizon scale, it works even in highly stochastic cases. For example, when the curvature perturbations are very large or the non-Gaussianities of the curvature perturbations are sizable, the perturbative expansion may break down but our algorithm enables to calculate the curvature perturbations. We apply it to two well-known inflation models, chaotic and hybrid inflation, in this paper. Especially for hybrid inflation, while the potential is very flat around the critical point and the standard perturbative computation is problematic, we successfully calculate the curvature perturbations.