On the cosmology of Weyl's gauge invariant gravity

TL;DR

This paper explores Weyl's gauge invariant gravity as a fundamental framework for vector inflation, showing it reduces to Einstein-Proca theory with spontaneous symmetry breaking, thus providing a potential theoretical basis for vector inflation.

Contribution

It demonstrates that Weyl's gauge invariant gravity naturally leads to Einstein-Proca theory with scalar fields, offering a fundamental support for vector inflation models.

Findings

Weyl's gauge gravity reduces to Einstein-Proca theory in four dimensions.

The scalar field exhibits a polynomial potential causing spontaneous symmetry breaking.

The theory does not support non-minimal coupling of the vector field to gravity.

Abstract

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.