  In this paper we investigate tensor fluctuations of the metric at the end of
a Higgs inflationary period in the context of a recently introduced complex
geometrical scalar-tensor theory of gravity. In our model the Higgs field has a
geometrical origin and the affine connection is determined by the Palatini's
principle. Additionally, we consider an extra contribution to the
tensor-fluctuations equation coming from the vacuum term in the energy momentum
tensor associated to the Higgs field. The Higgs potential is rescaled by the
non-canonicity function of the kinetic term of the field which is modified by
the symmetry group of the background geometry. We obtain a nearly scale
invariant spectrum and a scalar to tensor ratio in agreement with PLANCK 2018
cosmological results.
