Action approach to cosmological perturbations: the second-order metric in matterdominance

Abstract

We study nonlinear cosmological perturbations during post-inflationary evolution, usingthe equivalence between a perfect barotropic fluid and a derivatively coupled scalar fieldwith Lagrangian . Since this Lagrangian is just a special case ofk-inflation, this approach is analogous to the one employed in the study of non-Gaussianitiesfrom inflation. We use this method to derive the second-order metric during matter dominancein the comoving gauge directly as a function of the primordial inflationary perturbationζ. Going to Poisson gauge, we recover the metric previously derived in the literature.