  We obtain analytic solutions for the density contrast and the anisotropic
pressure in a multi-dimensional FRW cosmology with collisionless, massless
matter. These are compared with perturbations of a perfect fluid universe. To
describe the metric perturbations we use manifest gauge invariant metric
potentials. The matter perturbations are calculated by means of (automatically
gauge invariant) finite temperature field theory, instead of kinetic theory.
(Talk given at the Journ\'ees Relativistes '93, 5 -- 7 April, Brussels,
Belgium)
