Cosmology with matter diffusion
  We construct a viable cosmological model based on velocity diffusion of
matter particles. In order to ensure the conservation of the total
energy-momentum tensor in the presence of diffusion, we include a cosmological
scalar field $\phi$ which we identify with the dark energy component of the
Universe. The model is characterized by only one new degree of freedom, the
diffusion parameter $\sigma$. The standard $\Lambda$CDM model can be recovered
by setting $\sigma=0$. If diffusion takes place ($\sigma >0$) the dynamics of
the matter and of the dark energy fields are coupled. We argue that the
existence of a diffusion mechanism in the Universe can serve as a theoretical
motivation for interacting models. We constrain the background dynamics of the
diffusion model with Supernovae, H(z) and BAO data. We also perform a
perturbative analysis of this model in order to understand structure formation
in the Universe. We calculate the impact of diffusion both on the CMB spectrum,
with particular attention to the integrated Sachs-Wolfe signal, and on the
matter power spectrum $P(k)$. The latter analysis places strong constraints on
the magnitude of the diffusion mechanism but does not rule out the model.
