Cosmology of the non-local Proca theory

In this paper, we will consider cosmological implications of the Maxwell theory coupled to a non-local $U(1)$-symmetric term. It is well-known that the theory in flat space time, reduces to the Proca theory. However, it will be shown that in curved space time the resulting theory will differ from the coupled Einstein-Proca system. The cosmological perturbations on top of the de Sitter space-time is also considered and the dynamics of separate modes will be investigated in detail. Anisotropic cosmology of the model is also investigated and we will show that the behavior of the universe at late time satisfies the observational data and the model predicts an isotropic universe.