Green's function for gravitational waves in FRW spacetimes

TL;DR

This paper develops a method to calculate the retarded Green's function for gravitational waves in FRW spacetimes, revealing that background curvature causes support inside the light-cone, thus violating Huygens' principle.

Contribution

A novel analytical approach to compute the retarded Green's function for gravitational waves in general FRW spacetimes, including those with radiation and dust.

Findings

Green's function calculated for radiation and dust-filled FRW universes.

Green's function supports inside the light-cone when Ricci scalar curvature is non-zero.

Huygens' principle is violated in curved FRW spacetimes due to background curvature.

Abstract

A method for calculating the retarded Green's function for the gravitational wave equation in Friedmann-Roberson-Walker spacetimes, within the formalism of linearized Einstein gravity is developed. Hadamard's general solution to Cauchy's problem for second-order, linear partial differential equations is applied to the FRW gravitational wave equation. The retarded Green's function may be calculated for any FRW spacetime, with curved or flat spatial sections, for which the functional form of the Ricci scalar curvature $R$ is known. The retarded Green's function for gravitational waves propagating through a cosmological fluid composed of both radiation and dust is calculated analytically for the first time. It is also shown that for all FRW spacetimes in which the Ricci scalar curvatures does not vanish, $R \neq 0$, the Green's function violates Huygens' principle; the Green's function has support inside the light-cone due to the scatter of gravitational waves off the background curvature.