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

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.