Fully non-linear equivalence of delta N and covariant formalisms

TL;DR

This paper demonstrates the complete non-linear equivalence between the δN and covariant formalisms for superhorizon curvature perturbations, facilitating accurate non-Gaussianity calculations and clarifying isocurvature perturbation relations.

Contribution

It establishes the fully non-linear equivalence of δN and covariant formalisms, and clarifies their relation in multiple interacting fluid scenarios.

Findings

Confirmed the non-linear equivalence of formalisms for curvature perturbations.

Provided a framework for evaluating non-Gaussianities in either formalism.

Clarified the relation between curvature covector evolution and curvature perturbation in multi-fluid systems.

Abstract

We explicitly show the fully non-linear equivalence of the $\delta$N and the covariant formalisms for the superhorizon curvature perturbations, which enables us to safely evaluate the non-Gaussian quantities of the curvature perturbation in either formalism. We also discuss isocurvature perturbations in the covariant formalism and clarify the relation between the fully non-linear evolution of the curvature covector and that of the curvature perturbation for multiple interacting fluids.