A decoupled system of hyperbolic equations for linearized cosmological perturbations
Abstract
A decoupled system of hyperbolic partial differential equations for linear perturbations around any spatially flat FRW universe is obtained for a wide class of perturbations. The considered perturbing energy momentum-tensors can be expressed as the sum of the perturbation of a minimally coupled scalar field plus an arbitrary (weak) energy-momentum tensor which is covariantly conserved with respect to the background. The key ingredient in obtaining the decoupling of the equations is the introduction of a new covariant gauge which plays a similar role as harmonic gauge does for perturbations around Minkowski space-time. The case of universes satysfying a linear equation of state is discussed in particular, and closed analytic expressions for the retarded Green's functions solving the de Sitter, dust and radiation dominated cases are given.
Cite
@article{arxiv.gr-qc/0110071,
title = {A decoupled system of hyperbolic equations for linearized cosmological perturbations},
author = {J. Ramirez and S. Kopeikin},
journal= {arXiv preprint arXiv:gr-qc/0110071},
year = {2009}
}
Comments
6 pages, no figures, content enlarged