  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.
