Non-perturbative $\delta N$

TL;DR

This paper develops a non-perturbative approach within the $ abla$ formalism to calculate curvature perturbation correlations, especially useful for lattice simulations involving isocurvature modes during reheating.

Contribution

It introduces a non-perturbative $ abla N$ formalism that replaces derivatives with coefficients suitable for lattice simulation analysis.

Findings

Expressions for power spectrum and bispectrum derived

Validation of the non-perturbative expansion demonstrated

Method is well-suited for simulation applications

Abstract

We revisit the question of how to calculate correlations of the curvature perturbation, $\zeta$, using the $\delta N$ formalism when one cannot employ a truncated Taylor expansion of $N$. This problem arises when one uses lattice simulations to probe the effects of isocurvature modes on models of reheating. Working in real space, we use an expansion in the cross-correlation between fields at different positions, and present simple expressions for observables such as the power spectrum and the reduced bispectrum, $f_{\rm NL}$. These take the same form as those of the usual $\delta N$ expressions, but with the derivatives of $N$ replaced by non-perturbative $\delta N$ coefficients. We test the validity of this expansion and argue that our expressions are particularly well suited for use with simulations.