Quantum dynamics of the isotropic universe in metric gravity

We analyze the canonical quantum dynamics of the isotropic universe, as emerging from the Hamiltonian formulation of a metric 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 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 gravity appears more natural than in the Einsteinian picture.