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A closed set of equations for the evolution of linear perturbations of homogeneous, isotropic cosmological models can be obtained in various ways. The simplest approach is to assume a macroscopic equation of state, e.g., that of a perfect fluid. For a more refined description of the early Universe, a microscopic treatment is required. The purpose of this paper is to compare the approach based on classical kinetic theory to the more recent thermal-field-theory aproach. It is shown that in the high-temperature limit the latter describes cosmological perturbations supported by collisionless, massless matter, wherein it is equivalent to the kinetic theory approach. The dependence of the perturbations in a system of a collisionless gas and a perfect fluid on the initial data is discussed in some detail. All singular and regular solutions are found analytically.
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