Covariant cosmological perturbation dynamics in the inflationary universe

TL;DR

This paper simplifies the covariant linear perturbation theory in inflationary universes, deriving a conserved quantity and relating energy density perturbations to scalar field variables during inflation.

Contribution

It introduces a covariant conserved quantity on large scales and provides a new integral expression for energy density perturbations in inflationary cosmology.

Findings

Derived a closed integral expression for energy density perturbations.

Established a relation between perturbations at horizon reentry and during inflation.

Simplified the formalism of covariant perturbation dynamics in inflationary models.

Abstract

The linear cosmological perturbation theory of almost homogeneous and isotropic perfect fluid and scalar field universes is reconsidered and formally simplified. Using the existence of a covariant conserved quantity on large perturbation scales, a closed integral expression for comoving energy density perturbations is obtained for arbitrary equations of state. On this basis we establish a simple relation between fluid energy density perturbations at `reentry' into the horizon and the corresponding scalar field quantities at the first Hubble scale crossing during an early de Sitter phase of a standard inflationary scenario.