  We analyze some relevant features of the primordial Universe as viewed in the
Jordan frame formulation of the f(R)-gravity, especially when the potential
term of the non-minimally coupled scalar field is negligible. We start
formulating the Hamiltonian picture in the Jordan frame, using the 3-metric
determinant as a basic variable and we outline that its conjugated momentum
appears linearly only in the scalar constraint. Then, we construct the basic
formalism to characterize the dynamics of a generic inhomogeneous cosmological
model and specialize it in order to describe behaviors of the Bianchi
Universes, both on a classical and a quantum regime. As a fundamental issue, we
demonstrate that, when the potential term of the additional scalar mode is
negligible near enough to the initial singularity, the Bianchi IX cosmology is
no longer affected by the chaotic behavior, typical in vacuum of the standard
Einsteinian dynamics. In fact, the presence of stable Kasner stability region
and its actractive character are properly characterized. Finally, we
investigate the canonical quantization of the Bianchi I model, using as time
variable the non-minimally coupled scalar field and showing that the existence
of a conserved current is outlined for the corresponding Wheeler-DeWitt
equation. The behavior of a localized wave-packet for the isotropic Universe is
also evolved, demonstrating that the singularity is still present in this
revised quantum dynamics.
