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

Abstract

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 ϕ)^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 ζ. Going to Poisson gauge, we recover the metric previously derived in the literature.

16 pages. New version, typo fixed in eq. (91)

References in corpus (4)

• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• Non-gaussianity from the trispectrum in general single field inflation

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