Short wavelength analysis of the evolution of perturbations in a two-component cosmological fluid

The equations describing a two-component cosmological fluid with linearized density perturbations are investigated in the small wavelength or large k limit. The equations are formulated to include a baryonic component, as well as either a hot dark matter (HDM) or cold dark matter (CDM) component. Previous work done on such a system in static space-time is extended to reveal some interesting physical properties, such as the Jeans wave number of the mixture, and resonant mode amplitudes. A WKB technique is then developed to study the expanding universe equations in detail, and to see whether such physical properties are also of relevance in this more realistic scenario. The Jeans wave number of the mixture is reinterpreted for the case of an expanding background space-time. The various modes are obtained to leading order, and the amplitudes of the modes are examined in detail to compare to the resonances observed in the static space-time results. It is found that some conclusions made in the literature about static space-time results cannot be carried over to an expanding cosmology. (c) 2006 American Institute of Physics.