Covariant cosmological perturbation dynamics in the large-scale limit

TL;DR

This paper derives a covariant, gauge-invariant formula for large-scale cosmological perturbations, providing a unified description of their dynamics across different epochs in a flat universe.

Contribution

It introduces a general, closed-form integral expression for comoving energy density perturbations using covariant conserved quantities, applicable across various cosmological periods.

Findings

Provides a unified framework for large-scale perturbation analysis.

Derives a closed-form integral formula for gauge-invariant perturbations.

Discusses mode behavior in different cosmological epochs.

Abstract

Using the existence of a covariant conserved quantity on large perturbation scales in a spatially flat perfect fluid or scalar field universe, we present a general formula for gauge-invariantly defined comoving energy density perturbations which encodes the entire linear perturbation dynamics in a closed time integral. On this basis we discuss perturbation modes in different cosmological epochs.