Covariant perturbations in a multifluid cosmological medium

Peter K. S. Dunsby*, Marco Bruni, George F. R. Ellis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 gauge-invariant with respect to a Robertson-Walker 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 well-defined covariant and gauge-invariant 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 large-scale limit. We also correct a number of errors in the previous literature.

Original languageEnglish
Pages (from-to)54-74
Number of pages21
JournalAstrophysical Journal
Issue number1
Publication statusPublished - 10 Aug 1992


  • cosmology: theory
  • galaxies: formation
  • hydrodynamics
  • relativity


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