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

We study nonlinear cosmological perturbations during post-inflationary evolution, using the equivalence between a perfect barotropic fluid and a derivatively coupled scalar field with Lagrangian . 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 a function of the primordial inflationary perturbation ζ. Going to Poisson gauge, we recover the metric previously derived in the literature.