Gauge invariant fluctuations of the metric during inflation from a new scalar-tensor Weyl-integrable gravity model

Abstract

We investigate gauge invariant scalar fluctuations of the metric during inflation in a nonperturbative formalism in the framework of a recently formulated scalar-tensor theory of gravity, in which the geometry of space-time is that of a Weyl integrable manifold. We show that in this scenario the Weyl scalar field can play the role of the inflaton field. As an application of the theory, we examine the case of a power-law inflation. In this case, the quasi-scale invariance of the spectrum for scalar fluctuations of the metric is achieved for determined values of the parameter ω of the scalar-tensor theory. We stress the fact that in our formalism the physical inflaton field has a purely geometrical origin.