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We investigate gauge invariant scalar fluctuations of the metric duringinflation in a non-perturbative formalism in the framework of a recentlyintroduced scalar-tensor theory of gravity formulated on a Weyl-Integrablegeometry. We found that the Weyl scalar field can play the role of the inflatonfield in this theory. As an application we study the case of a power lawinflation. In this case the quasi-scale invariance of the spectrum for scalarfluctuations of the metric is achieved for determined values of the $\omega$parameter of the scalar-tensor theory. In our formalism the physical inflatonfield has a geometrical origin.

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