The phenomenology of Quantum Bounce in the Klein-Gordon, Wheeler-DeWitt and Dirac formalisms

TL;DR

This paper explores the concept of Quantum Bounce across different quantum cosmology formalisms, demonstrating its applicability in Klein-Gordon, Wheeler-DeWitt, and Dirac frameworks through various models and calculations.

Contribution

It provides a unified analysis of Quantum Bounce phenomena in multiple formalisms, including new insights into volume operator behavior and Kasner transitions.

Findings

Quantum Bounce describes scattering between universe branches in Klein-Gordon formalism.

Volume operator analysis supports the Quantum Big Bounce in Wheeler-DeWitt framework.

Quantum Bounce models can describe Kasner transitions in Bianchi models.

Abstract

We investigate the different meanings that the concept of Quantum Bounce acquires in various formalisms. The original idea refers to the phenomenology that appears in the Klein-Gordon framework when homogeneous cosmologies are considered. In that case, the Quantum Bounce describes the quantum scattering between a collapsing and an expanding Universe branch, and therefore provides a quantum description of the semiclassical Big Bounce mechanism. Here, we show that the proposal of the Quantum Big Bounce is well-grounded, thanks to the computation of the volume operator mean values and its standard deviation in the Wheeler-DeWitt framework for the isotropic case. Then, we analyze the Bianchi models in the Dirac approach, now showing that the Quantum Bounce concept can be implemented to describe the Kasner transitions of the Belinski-Khalatnikov-Lifshitz map at a quantum level. In summary, the quantum scattering framework borrowed from particle physics can serve as a good model for different cosmological scenarios, which can exhibit scalar-like or fermionic-like behaviours depending on how the anisotropies are described in the dynamics.