Temperature fluctuations in an inhomogeneous diffusive fluid

Abstract

We discuss metric perturbations of the relativistic diffusion equation around the homogeneous Jüttner equilibrium of massless particles in a homogenous expanding universe. We describe the perturbations corresponding to the gravitational wave background. We show that the lowest order perturbation can be treated as a variation of temperature. We derive a formula expressing temperature fluctuations in terms of the diffusion and tensor power spectrum. We discuss the multipole expansion of the fluctuations in the presence of diffusion.