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

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.

28 pages, no figures. v2: Added a summary subsection 4.3 with further discussion of the results. Generalized all super-horizon results of section 4 and appendix A to exact ones. Other minor textual changes and references added. Conclusions unchanged. Matches published version

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• A short note on the curvature perturbation at second order
• Momentum dependence of the bispectrum in two-field inflation
• Non-Gaussianity in two-field inflation beyond the slow-roll approximation
• Covariant second-order perturbations in generalized two-field inflation
• Non-Gaussianity in Cosmology: from Inflation to the CMB