Conserved cosmological perturbations

Abstract

A conserved cosmological perturbation is associated with each quantity whose local evolution is determined entirely by the local expansion of the Universe. It may be defined as the appropriately normalised perturbation of the quantity, defined using a slicing of spacetime such that the expansion between slices is spatially homogeneous. To first order, on super-horizon scales, the slicing with unperturbed intrinsic curvature has this property. A general construction is given for conserved quantities, yielding the curvature perturbation $ζ$ as well as more recently-considered conserved perturbations. The construction may be extended to higher orders in perturbation theory and even into the non-perturbative regime.