Cosmological perturbation theory of primordial compact sources
Phys. Rev. D 113, 084038 – Published 16 April, 2026
DOI: https://doi.org/10.1103/yyk2-syxj
Abstract
We construct a position-space cosmological perturbation theory around spatially flat Friedmann-Lemaître-Robertson-Walker geometries that allows one 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 [Classical Quantum Gravity 34, 035009 (2017), Classical Quantum Gravity 34, 194001 (2017)]. 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.
