  We investigate a very general class of cosmological models with scalar fields
non-minimally coupled to gravity. A particular representative in this class is
given by the non-minimal Higgs inflation model in which the Standard Model
Higgs boson and the inflaton are described by one and the same scalar particle.
While the predictions of the non-minimal Higgs inflation scenario come
numerically remarkably close to the recently discovered mass of the Higgs
boson, there remains a conceptual problem in this model that is associated with
the choice of the cosmological frame. While the classical theory is independent
of this choice, we find by an explicit calculation that already the first
quantum corrections induce a frame dependence. We give a geometrical
explanation of this frame dependence by embedding it into a more general field
theoretical context. From this analysis, some conceptional points in the long
lasting cosmological debate: "Jordan frame vs. Einstein frame" become more
transparent and in principle can be resolved in a natural way.
