The Geometric Proca–Weyl Field as a Candidate for Dark Matter

We consider the Weyl invariant theory of gravity as an alternative approach to the problem of the origin of dark matter. According to this theory, the geometric Weyl 1-form effectively behaves as a Proca field. In this work, our starting point is to consider the existence of a gas of Weyl–Proca particles in a Bose–Einstein condensate and investigate its behavior in a cosmological context. The results obtained show that, for appropriate values of the free parameter of the model, the Weyl field behaves approximately as a dust fluid in the matter-dominated era as expected for a dark matter candidate.