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

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