Towards solving generic cosmological singularity problem

TL;DR

This paper investigates the quantum big bounce in loop quantum cosmology, analyzing the dynamics and uncertainties of physical observables, and discusses the implications for understanding the generic cosmological singularity.

Contribution

It provides a detailed construction of the self-adjoint Hamiltonian and evolution operator for the quantum FRW model, advancing the understanding of the big bounce transition.

Findings

Expectation values of observables are well-defined during the bounce

Dispersion of observables respects the Heisenberg uncertainty principle

The true nature of the bounce requires quantization of the more general BKL scenario

Abstract

The big bounce transition of the quantum FRW model in the setting of loop quantum cosmology is presented. We determine the physical self-adjoint Hamiltonian generating the dynamics. It is used to define, via the Stone theorem, an evolution operator. We examine properties of expectation values of physical observables in the process of the quantum big bounce transition. The dispersion of observables are studied in the context of the Heisenberg uncertainty principle. We suggest that the real nature of the bounce may become known only after we quantize the Belinskii-Khalatnikov-Lifshitz scenario, which concerns the generic cosmological singularity.