Gauge invariant perturbations in multi-component fluid cosmologies

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Abstract
An alternative approach to the study of cosmological density perturbations in cosmology has been presented. Covariant and gauge invariant quantities were defined that characterize density inhomogeneities in an almost-uniform model universe and propagation equations were derived for these quantities in the case of a general perfect fluid. The author extends this work to the case of an imperfect fluid and derives generalizations of these equations. The author then applies the theory to a multi-component fluid, in particular to the case where the background is described by a spatially flat Friedmann-Lemaitre-Robertson-Walker universe model containing a mixture of non-interacting dust and radiation. Solutions are obtained for the comoving fractional density gradient, the energy flux and the relative velocity in the centre of mass frame which include new modes linking the density gradient to the vorticity.