  We analyse the canonical quantum dynamics of the isotropic universe, as
emerging from the Hamiltonian formulation of a metric f(R) gravity, viewed in
the Jordan frame. The canonical method of quantization is performed by solving
the Hamiltonian constraint before quantizing and adopting like a relational
time the non-minimally coupled scalar field emerging in the Jordan frame. The
resulting Schr\"oedinger evolution is then investigated both in the vacuum and
in the presence of a massless scalar field, though as the kinetic component of
an inflaton. We show that, in vacuum, the morphology of localized wave packets
is that of a non-spreading profile up to the cosmological singularity. When the
external scalar field is included into the dynamics, we see that the wave
packets acquire the surprising feature of increasing localization of the
universe volume, as it expands. This result suggests that in the metric f(R)
formulation of gravity, a spontaneous mechanism arises for the universe
classicization. Actually, when the phase space of the scalar field is fully
explored, such an increasing localization in the Universe volume is valid up to
a given value of the time, i.e. of the non-minimally coupled mode after which
the wave packets spread again. We conclude our analysis by inferring that
before this critical transition age is reached, the inflationary phase could
take place, here modelled via a cosmological constant. This point of view
provides an interesting scenario for the transition from a Planckian Universe
to a classical de-Sitter phase, which in the f(R) gravity appears more natural
than in the Einsteinian picture.
