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

Abstract

We describe energy-momentum conservation in relativistic perturbation theory in general Friedmann-Robertson-Walker ͑FRW͒ 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 numerically͒ useful context.

Cosmological perturbation theory, instantaneous gauges, and local inertial frames

“…The resulting 'KBL superpotential', using the designation by Julia and Silva [17], was found, after applying certain natural criteria, to be unambigous and most satisfactory in spacetimes with or without a cosmological constant, in any spacetime dimension D ≥ 3 (see [17], [18]). It also found applications in the recent studies of the causal generation of cosmological perturbations seeding large-scale structure formation and of the back reactions in slow-roll inflation (see [19], [20], and references therein).…”

Summary of cosmology workshop

“…D-brane inflation) of high energy physics inspired inflationary scenarios terminate with the production of topological defects. In order to investigate the observational implications of such models, G. Amery described a complete 4-d synchronous gauge formalism that may include non-zero curvature and cosmological constants, multiple scalar fields, and topological defects or other active sources [29]. The formalism provides a concise and geometrically sound description of energy-momentum conservation on all scales, from which appropriate initial conditions may be obtained.…”