Marco Valerio Battisti

Title: Quantum Cosmology: Evolutionary Quantum Dynamics and Generalized Uncertainty Principle

Speaker: Marco Valerio Battisti (battisti@icra.it)

Co-author: Giovanni Montani

ICRANet  - Physics Department University of Rome ``La Sapienza''

Abstract: The comparison of two different quantum cosmological approaches is investigated. We consider a Schrodinger dynamics for the gravitational field associated to a Bianchi IX cosmological model and then we solve the corresponding eigenvalue problem. We show that, form a phenomenological point of view, an Evolutionary Quantum Cosmology overlaps the Wheeler-De Witt approach.

This model is compared to a quantization of the same cosmological model using a generalized uncertainty relation. In particular we quantize the anisotropy variable of the Taub cosmological model, as well as Bianchi IX, using generalized commutation relations that imply that we have a minimal anisotropy uncertainty.

Riccardo Benini

Title: "Influcence of a Vector Field on the Mixmaster Dynamics"

Authors: Riccardo Benini, Giovanni Montani

Speaker: Riccardo Benini

Abstract: We show that in multidimensional gravity, vector fields completely determine the structure and properties of singularity. It turns out that in the presence of a vector field the oscillatory regime exists in all spatial dimensions and for all homogeneous models. By analysing the Hamiltonian equations we derive the Poincar´e return

map associated with the Kasner indexes and fix the rules according to which the Kasner vectors rotate.

In correspondence to a fourdimensional spacetime, the oscillatory regime here constructed overlaps the usual Belinski-Khalatnikov-Liftshitz one.