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

##### Authors
Boubekeur, Lotfi
Creminelli, Paolo
Norena, Jorge
Vernizzi, Filippo
##### Description
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.
Comment: 16 pages. New version, typo fixed in eq. (91)
##### Keywords
Astrophysics, General Relativity and Quantum Cosmology, High Energy Physics - Theory