  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.
