Cosmological perturbation theory and conserved quantities in the large-scale limit

TL;DR

This paper revisits linear cosmological perturbation theory, introducing covariant, gauge-invariant variables to better understand conserved quantities on large scales in various background geometries.

Contribution

It provides a simplified, covariant framework for analyzing perturbations and clarifies the conditions for conserved quantities in curved and flat universes.

Findings

Conserved quantities can be expressed in terms of energy density gradients.

Large-scale perturbations are best described on hypersurfaces of constant expansion or curvature.

The formalism applies to universes with nonzero background curvature.

Abstract

The linear cosmological perturbation theory of an almost homogeneous and isotropic perfect fluid universe is reconsidered and formally simplified by introducing new covariant and gauge-invariant variables with physical interpretations on hypersurfaces of constant expansion, constant curvature or constant energy density. The existence of conserved perturbation quantities on scales larger than the Hubble scale is discussed. The quantity which is conserved on large scales in a flat background universe may be expressed in terms of the fractional, spatial gradient of the energy density on constant expansion hypersurfaces or, alternatively, with the help of expansion or curvature perturbation variables on hypersurfaces of constant energy density. For nonvanishing background curvature the perturbation dynamics is most suitably described in terms of energy density perturbations on hypersurfaces of constant curvature.