A decoupled system of hyperbolic equations for linearized cosmological perturbations

TL;DR

This paper derives a decoupled hyperbolic PDE system for linear cosmological perturbations in flat FRW universes, introducing a new covariant gauge and providing explicit Green's functions for key cosmological models.

Contribution

It introduces a novel covariant gauge that enables decoupling of perturbation equations in flat FRW universes with various matter contents.

Findings

Decoupled hyperbolic PDE system for perturbations derived.

Explicit Green's functions provided for de Sitter, dust, and radiation cases.

Applicable to a wide class of perturbing energy-momentum tensors.

Abstract

A decoupled system of hyperbolic partial differential equations for linear perturbations around any spatially flat FRW universe is obtained for a wide class of perturbations. The considered perturbing energy momentum-tensors can be expressed as the sum of the perturbation of a minimally coupled scalar field plus an arbitrary (weak) energy-momentum tensor which is covariantly conserved with respect to the background. The key ingredient in obtaining the decoupling of the equations is the introduction of a new covariant gauge which plays a similar role as harmonic gauge does for perturbations around Minkowski space-time. The case of universes satysfying a linear equation of state is discussed in particular, and closed analytic expressions for the retarded Green's functions solving the de Sitter, dust and radiation dominated cases are given.