Exploring non-linear cosmological matter diffusion coefficients

Since microscopic velocity diffusion can be incorporated into general relativity in a consistent way, we study cosmological background solutions when the diffusion phenomena takes place in an expanding universe. Our focus here relies on the nature of the diffusion coefficient $\sigma$ which measures the magnitude of such transport phenomena. We test dynamics where $\sigma$ has a phenomenological dependence on the scale factor, the matter density, the dark energy and the expansion rate.