Cosmological perturbation theory of primordial compact sources

TL;DR

This paper develops a position-space cosmological perturbation theory to model localized primordial sources of gravitational waves, providing exact solutions and Green's functions for various cosmologies.

Contribution

It introduces a gauge-based approach avoiding scalar-vector-tensor decomposition and derives explicit Green's functions for power law cosmologies.

Findings

Exact Green's function expressed as a hypergeometric function.

Closed form of linearized metric perturbation up to quadrupolar order.

Sources cannot be generally localized due to cosmic fluid fluctuations.

Abstract

We construct a position-space cosmological perturbation theory around spatially flat Friedmann-Lema\^itre-Robertson-Walker geometries that allows to model localized primordial sources of gravitational waves. The equations of motion are decoupled using a generalized harmonic gauge, which avoids the use of a scalar-vector-tensor decomposition. We point out that sources cannot generically be defined in a compact domain due to fluctuations of the cosmic perfect fluid. For power law cosmologies, we obtain the exact Green's function necessary to solve for all metric perturbations in terms of a hypergeometric function, which matches with a Green's function derived earlier by Chu. This allows us to derive the closed form expression of the linearized metric perturbation generated by sources up to quadrupolar order in the multipolar expansion.