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A decoupled system of hyperbolic equations for linearized cosmological perturbations

J. Ramirez·S. Kopeikin
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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.

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J. Ramirez, S. Kopeikin. 2002-02-01. A decoupled system of hyperbolic equations for linearized cosmological perturbations. https://doi.org/10.1016/s0370-2693(02)01471-5

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