Is Bianchi I a Bouncing Cosmology in the Wheeler-DeWitt picture?

TL;DR

This paper investigates whether Bianchi I cosmology can be described as a quantum bouncing universe within the Wheeler-DeWitt framework, highlighting the probabilistic nature of the bounce and the limitations of semiclassical approximations.

Contribution

It introduces a quantum transition amplitude for Bianchi I models, demonstrating a probabilistic Big Bounce and analyzing wave packet spreading near the singularity.

Findings

Transition probability peaks when pre- and post-bounce momenta are similar.

Wave packets spread near the singularity, losing semiclassical predictability.

The bounce is described as a probabilistic transition rather than a deterministic event.

Abstract

We provide a quantum picture for the emergence of a bouncing cosmology, according to the idea that a semiclassical behavior of the Universe towards the singularity is not available in many relevant Minisuperspace models. In particular, we study the Bianchi I model in vacuum adopting the isotropic Misner variable as an internal clock for the quantum evolution. The isomorphism between the Wheeler-DeWitt equation in this Minisuperspace representation and the Klein-Gordon one for a relativistic scalar field allows to identify the positive and negative frequency solutions as associated to the collapsing and expanding Universe respectively. We clarify how any Bianchi I localized wave packet unavoidably spreads when the singularity is approached and therefore the semiclassical description of the model evolution in the Planckian region loses its predictability. Then, we calculate the transition amplitude that a collapsing Universe is turned into an expanding one, according to the standard techniques of relativistic quantum mechanics, thanks to the introduction of an ekpyrotic-like matter component which mimics a time-dependent potential term and breaks the frequency separation. In particular, the transition probability of this "Quantum Big Bounce" acquires a maximum value when the mean values of the momenta conjugate to the anisotropies in the collapsing Universe are close enough to the corresponding mean values in the expanding one, depending on the variances of the in-going and out-going Universe wave packets. This symmetry between the pre-Bounce and post-Bounce mean values reflects what happens in the semiclassical bouncing cosmology, with the difference that here the connection of the two branches takes place on a pure probabilistic level.