Applications to cosmological models of a complex scalar field coupled to a U(1) vector gauge field

We consider the Abelian model of a complex scalar field coupled to a gauge field within the framework of General Relativity and search for cosmological solutions. For this purpose we assume a homogeneous, isotropic and uncharged Universe and a homogeneous scalar field. This model may be inserted in several contexts in which the scalar field might act as inflaton or quintessence, whereas the gauge field might play the role of radiation or dark matter, for instance. Particularly, we propose two such models: (i) in the first, the inflaton field decays to massive vector bosons that we regard as dark-matter; (ii) in the second, due to its coupling to radiation the scalar field is displaced from its ground state and drives an accelerated expansion of the Universe, playing the role of quintessence. We observe that the equations are quite simplified and easier to be solved if we assume a roughly monochromatic radiation spectrum.