Conserved cosmological perturbations

TL;DR

The paper presents a geometric, gauge-invariant framework showing that conserved cosmological perturbations arise from local continuity equations when evaluated on uniform integrated expansion slices. The central result is that the curvature perturbation $\\zeta$ is conserved on super-horizon scales for adiabatic perturbations, with generalizations to separately conserved densities $\\zeta_i$ and conserved number densities $\\tilde{\\zeta}_i$, and a second-order extension for non-Gaussian considerations. The analysis demonstrates that the uniform-$N$ (flat) slicing yields a robust, threading-independent construction of these conserved quantities, and shows that super-horizon shear is negligible, validating the conservation on large scales. These results have direct implications for connecting inflationary initial conditions to late-time observables, including isocurvature perturbations and curvaton scenarios, and provide a framework extendable to non-perturbative regimes. Overall, the work deepens the understanding of how local conservation laws govern the evolution of cosmological perturbations across different epochs and perturbation orders.

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.