Gauge-invariant perturbations at second order in two-field inflation

TL;DR

This paper develops a comprehensive framework for second-order gauge-invariant perturbations in two-field inflation, enabling precise calculations of non-Gaussianity beyond slow-roll and super-horizon scales.

Contribution

It introduces exact cubic actions for second-order perturbations in multiple gauges, advancing the analysis of non-Gaussian features in inflationary models.

Findings

Derived the exact cubic action for second-order perturbations.

Established relations between different perturbation quantities.

Provided tools for calculating non-Gaussianity at any scale.

Abstract

We study the second-order gauge-invariant adiabatic and isocurvature perturbations in terms of the scalar fields present during inflation, along with the related fully non-linear space gradient of these quantities. We discuss the relation with other perturbation quantities defined in the literature. We also construct the exact cubic action of the second-order perturbations (beyond any slow-roll or super-horizon approximations and including tensor perturbations), both in the uniform energy density gauge and the flat gauge in order to settle various gauge-related issues. We thus provide the tool to calculate the exact non-Gaussianity beyond slow-roll and at any scale.