Construction of the conserved ζζ via the effective action for perfect fluids

We consider the problem of how to construct the curvature perturbation ζζ, which is expected to be time independent on super-horizon scales to nonlinear level; in particular we concentrate on the case where the existence of such conserved ζζ is guaranteed: a universe dominated by a perfect fluid with adiabatic pressure. We have used a low energy/long wavelength effective action to model the fluid sector and coupled it to the Einstein gravity. This setup enables us to verify explicitly the assumption of “local homogeneity and isotropy” used in previous literature. As a corollary, we also show that the nonlinearly defined graviton field γijγij is conserved outside the horizon in the same manner as ζζ is.