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We analyze 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 nonminimally coupled scalar field emerging in the Jordan frame. The resulting Schrödinger 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 nonspreading 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 classicalization. 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 nonminimally 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 modeled 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. [ABSTRACT FROM AUTHOR]

We analyze the dynamics of a Taub cosmological model in the presence of a massless minimally coupled scalar field and a cosmological constant, in the limit when both the universe volume and the scalar field live in a quasiclassical approximation. In other words, we study the dynamics of a quantum small anisotropy evolving on a de Sitter background and in the presence of a kinetic term of the inflaton field. We demonstrate that the quantum anisotropy exponentially decays during the universe expansion, approaching a finite and small value. This result suggests that the quantum isotropization of the universe during a de Sitter phase is much weaker than the corresponding classical evolution, favoring the survival of certain degree of anisotropy to the de Sitter phase. Finally we analyze the case when also the scalar field is considered as quantum variable, by showing how its variance naturally spreads because of no potential term significantly affects its dynamics. This behavior results to be different from the anisotropy which is subjected to the potential coming out from the spatial curvature. [ABSTRACT FROM AUTHOR]