Causal perturbation theory in general FRW cosmologies: Energy-momentum conservation and matching conditions

We describe energy-momentum conservation in relativistic perturbation theory in general Friedmann-Robertson-Walker (FRW) backgrounds with causal source terms, such as the presence of cosmic defect networks. A prescription for a linear energy-momentum pseudotensor in a curved FRW universe is provided, and it is decomposed using eigenfunctions of the Helmholtz equation. Conserved vector densities are constructed from the conformal geometry of these spacetimes and related to our pseudotensor, demonstrating the equivalence of these two approaches. We also relate these techniques to the role played by residual gauge freedom in establishing matching conditions at early phase transitions, which we can express in terms of components of our pseudotensor. This formalism is concise and geometrically sound on both sub- and superhorizon scales, thus extending existing work to a physically (and numerically) useful context. © 2003 The American Physical Society.