Action approach to cosmological perturbations: the second-order metric in matter dominance
Abstract
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 [-(\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 a function of the primordial inflationary perturbation ζ. Going to Poisson gauge, we recover the metric previously derived in the literature.
- Publication:
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Journal of Cosmology and Astroparticle Physics
- Pub Date:
- August 2008
- DOI:
- 10.1088/1475-7516/2008/08/028
- arXiv:
- arXiv:0806.1016
- Bibcode:
- 2008JCAP...08..028B
- Keywords:
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- Astrophysics;
- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 16 pages. New version, typo fixed in eq. (91)