Kinetics of small perturbations in an isotropic world - III. Long-wavelength perturbations in an ultrarelativistic gas

Long-wavelength gravitational perturbations are studied in an isotropic expanding universe filled with an ultrarelativistic gas. A kinetic study in the collisionless approximation shows that scalar and vector perturbations which appear at a time η0 ≪ 1/n, where N is the wave vector and η is the time coordinate x4, grow if the perturbation of the macroscopic momentum density of the gas at time η0 is nonvanishing. The growth continues until the time η1=27η0, at which the perturbation of the macroscopic momentum density of the gas vanishes. A solution is also derived for tensor perturbations in the limit nη ≪ 1. © 1978 Plenum Publishing Corporation