Abstract
We consider the Abelian model of a complex scalar field coupled to a gauge field within theframework of General Relativity and search for cosmological solutions. For this purpose weassume 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 asinflaton or quintessence, whereas the gauge field might play the role of radiation or darkmatter, for instance. In particular, we propose two such models: (i) in the first, theinflaton 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 fromits ground state and drives an accelerated expansion of the Universe, playingthe role of quintessence. We observe that the equations are quite simplified andbecome easier to solve if we assume a roughly monochromatic radiation spectrum.
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