Kinetics of small perturbations in an isotropic world

Abstract

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 timeη ₀ ≪ 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 timeη ₀ is nonvanishing. The growth continues until the timeη ₁=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.