ON THE COSMOLOGY OF WEYL'S GAUGE INVARIANT GRAVITY

Recently the vector inflation has been proposed as the alternative to inflationary models based on scalar bosons and quintessence scalar fields. In the vector inflationary model, the vector field non-minimally couples to gravity. We should, however, inquire if there exists a relevant fundamental theory which supports the inflationary scenario. We investigate the possibility that Weyl's gauge gravity theory could be such a fundamental theory. That is the reason why the Weyl's gauge invariant vector and scalar fields are naturally introduced. After rescaling the Weyl's gauge invariant Lagrangian to the Einstein frame, we find that in four dimensions the Lagrangian is equivalent to Einstein-Proca theory and does not have the vector field non-minimally coupled to gravity, but has the scalar boson with a polynomial potential which leads to the spontaneously symmetry breakdown.