Covariant Perturbations in a Multifluid Cosmological Medium
Abstract
In a series of recent papers, a new covariant formalism was introduced to treat inhomogeneities in any spacetime. The variables introduced in these papers are gaugeinvariant with respect to a RobertsonWalker background spacetime because they vanish identically in such models, and they have a transparent physical meaning. Exact evolution equations were found for these variables, and the linearized form of these equations were obtained, showing that they give the standard results for a barotropic perfect fluid. In this paper we extend this formalism to the general case of multicomponent fluid sources with interactions between them. We show, using the tilted formalism of King & Ellis, that choosing either the energy frame or the particle frame gives rise to a set of physically welldefined covariant and gaugeinvariant variables which describe density and velocity perturbations, both for the total fluid and its constituent components. We then derive a complete set of equations for these variables and show, through harmonic analysis, that they are equivalent to those of Bardeen and of Kodama and Sasaki. We discuss a number of interesting applications, including the case where the universe is filled with a mixture of baryons and radiation, coupled through Thomson scattering, and we derive solutions for the density and velocity perturbations in the largescale limit. We also correct a number of errors in the previous literature.
 Publication:

The Astrophysical Journal
 Pub Date:
 August 1992
 DOI:
 10.1086/171630
 Bibcode:
 1992ApJ...395...54D
 Keywords:

 Galactic Evolution;
 Hydrodynamics;
 Perturbation Theory;
 Relativistic Theory;
 Covariance;
 Ideal Fluids;
 Thomson Scattering;
 Astrophysics;
 COSMOLOGY: THEORY;
 GALAXIES: FORMATION;
 HYDRODYNAMICS;
 RELATIVITY