Construction of the Conserved Non-linear Zeta via the Effective Action for Perfect Fluids

TL;DR

This paper develops a nonlinear construction of the curvature perturbation  that remains conserved on super-horizon scales in a universe dominated by a perfect fluid, using an effective action approach that includes vector and tensor modes.

Contribution

It introduces a novel method to construct  nonlinearly without assuming local homogeneity or isotropy, extending previous work to include vector and tensor perturbations.

Findings

 is conserved outside the horizon at nonlinear levels.

The nonlinearly defined graviton _{ij} is also conserved outside the horizon.

The effective action approach models the fluid sector without simplifying assumptions.

Abstract

We consider the problem of how to construct the curvature perturbation $\zeta$ to nonlinear levels, which is expected to evolve time independently on super-horizon scales; in particular we concentrate on the situation where the universe is dominated by a perfect fluid. We have used a low energy/long wavelength effective action to model the fluid sector. Different from previous work, our approach assumes neither the absence of vector and tensor perturbations nor ``local homogeneity and isotropy''. As a corollary, we also show that the nonlinearly defined graviton field $\gamma_{ij}$ is conserved outside the horizon in the same manner as $\zeta$ is.