Quantum Big Bounce in Wheeler-DeWitt scattering theory: Ekpyrotic and LQC-like transitions

TL;DR

This paper formulates a quantum Big Bounce scenario for a closed universe with a scalar field, revealing two types of transitions and highlighting the limitations of Wheeler-DeWitt theory at high energies.

Contribution

It provides a rigorous covariant formulation of the quantum Big Bounce, identifying two distinct bouncing scenarios and analyzing their energy regimes within Wheeler-DeWitt theory.

Findings

Identifies LQC-like and ekpyrotic transition scenarios.

Shows WDW theory's validity limit at high energies.

Demonstrates quantum avoidance of singularity in WDW framework.

Abstract

We present a rigorous formulation of the Quantum Big Bounce for the closed isotropic Universe, filled with a self-interacting scalar field, that emerges from the interaction with an ekpyrotic potential. Working in a covariant approach to the minisuperspace, we demonstrate the quantum equivalence between parametrizations in terms of the logarithmic scale factor and the volume variable. The analogy between the Wheeler-DeWitt equation and the Klein-Gordon equation, alongside a proper definition of asymptotic states, allows the identification of two different bouncing scenarios: one in which the transition occurs over a fixed direction of the internal time arrow, corresponding to a LQC-like scenario, and one involving a reversal of the internal time flow. The high-energy divergence in the former case shows the incompleteness of the WDW theory and the need for regularization. Therefore, the WDW theory is valid up to a given energy threshold. The latter transition, corresponding to an ekpyrotic scenario, is instead well-posed at any energy scale at the first perturbative order. While the Ashtekar school Big Bounce is expected to be recovered when high-energy corrections are included in this scheme, the WDW alone can avoid the cosmological singularity in a quantum mechanical fashion.