  We study the dynamics of scalar metric fluctuations in a non-perturbative
variational formalism recently introduced, by which the dynamics of an
geometrical scalar field $\theta$, describes the quantum geometrical effects on
a Weylian-like manifold with respect to a background Riemannian space-time. In
this letter we have examined an example in the framework of inflationary
cosmology. The resulting spectral predictions are in very good agreement with
observations and other models of inflation.
