Eleonora Giovannnetti "Bianchi IX anisotropies in a bouncing scenario: a quantum approach"

Wednesday 13 Nov 2024, 12:30 → 14:00 Europe/Rome

Sala Fiore (Marconi)

Bianchi IX anisotropies in a bouncing scenario: a quantum approach

 

We study the implementation of Polymer Quantum Mechanics (PQM) to a system decomposed into a quasi-classical background and a small quantum subsystem, according to the original Vilenkin proposal. Then, we provide a Minisuperspace application of the theory, first considering a Bianchi I cosmology and then extending the analysis to a Bianchi IX model in the limit of small anisotropies. In both these cases, the quasi-classical background is identified with an isotropic bouncing Universe whereas the small quantum subsystem contains the anisotropic degrees of freedom. When the Big Bounce scenario is considered, we obtain that in the Bianchi I model the anisotropies standard deviation is regular but still increases indefinitely, whereas in the presence of the harmonic Bianchi IX potential the same quantity is bounded and oscillates around a constant value. As a consequence, we demonstrate that the picture of a semiclassical isotropic Bounce can be extended to more general cosmological settings, if the spatial curvature becomes relevant when the anisotropic degrees of freedom are still small quantum variables.                                                     

Finally, we provide a new picture for the emergence of a bouncing cosmology at a pure quantum level, according to the idea that a semiclassical behaviour of the Universe towards the singularity is not available when the generic cosmological solution is taken into account. In particular, we highlight the isomorphism between the Wheeler-DeWitt equation for the Bianchi models in the Misner variables and the Klein-Gordon equation for a relativistic scalar field. We identify the positive and negative frequency solutions with the collapsing and expanding Universe respectively, and then we calculate the transition amplitude between a collapsing Universe and an expanding one for the Bianchi I model, according to the standard techniques of relativistic quantum mechanics. This framework is also improved by using the Dirac equation, in order to study the quantum properties of the BKL map in the Bianchi IX model.

Link to the papers: https://arxiv.org/abs/2302.02469, https://arxiv.org/abs/2203.01062.