On Singularity Resolution in Quantum Gravity

TL;DR

This paper explores a new loop quantum gravity-inspired quantization of cosmological models, demonstrating that it can resolve classical singularities by avoiding infinite densities in quantum dynamics.

Contribution

Introduces a novel quantization method for quantum cosmology inspired by loop quantum gravity, showing singularity avoidance through a difference operator Hamiltonian.

Findings

Existence of a densely defined inverse scale factor operator

Hamiltonian acts as a difference operator on basis states

Quantum dynamics avoids the classical singularity

Abstract

We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity programme, and is based on an alternative to the Schr\"odinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute "singularity resolution" in quantum gravity.