Action approach to cosmological perturbations: the 2nd order metric in matter dominance

TL;DR

This paper develops a method to derive the second order metric during matter dominance in cosmology, linking nonlinear perturbations to primordial inflationary fluctuations, and confirms previous results using an alternative approach.

Contribution

It introduces an action-based approach to compute second order cosmological metrics during matter dominance, connecting perfect fluid and scalar field descriptions.

Findings

Derived the second order metric in comoving gauge as a function of primordial perturbations

Recovered known metric results in Poisson gauge, confirming consistency

Provided a new derivation method applicable to nonlinear cosmological perturbations

Abstract

We study nonlinear cosmological perturbations during the post-inflationary evolution, using the equivalence between a perfect barotropic fluid and a derivatively coupled scalar field with Lagrangian [-(\partial \phi)^2]^[(1+w)/2w]. Since this Lagrangian is just a special case of k-inflation, this approach is analogous to the one employed in the study of non-Gaussianities from inflation. We use this method to derive the second order metric during matter dominance in the comoving gauge directly as function of the primordial inflationary perturbation \zeta. Going to Poisson gauge, we recover the metric previously derived in the literature.