Alternative $k=-1$ loop quantum cosmology

TL;DR

This paper proposes a new loop quantum cosmology quantization for the $k=-1$ model, treating Euclidean and Lorentzian terms separately, resulting in a quantum bounce replacing the classical big bang singularity.

Contribution

It introduces an alternative quantization method for the $k=-1$ model, aligning with full loop quantum gravity treatment, and constructs a Hamiltonian operator with correct classical limits.

Findings

Quantum bounce replaces big bang singularity.

Hamiltonian operator has correct classical limit.

New dynamics differ from previous schemes.

Abstract

An alternative quantization of the gravitational Hamiltonian constraint of the $k=-1$ Friedmann-Robertson-Walker model is proposed by treating the Euclidean term and the Lorentzian term independently, mimicking the treatment of full loop quantum gravity. The resulting Hamiltonian constraint operator for the $k=-1$ model with a massless scalar field is successfully constructed, and is shown to have the corrected classical limit. Compared to the former quantization schemes in the literature where only the Euclidean term is quantized, the new quantum dynamics of the $k=-1$ model with a massless scalar field indicates that the classical big-bang singularity is replaced by an asymmetric quantum bounce.