Absence of Singularity in Loop Quantum Cosmology

TL;DR

This paper demonstrates that loop quantum cosmology naturally resolves the classical singularity by showing quantum geometric effects lead to a non-diverging inverse scale factor and a well-defined evolution through the classical singularity.

Contribution

It provides a detailed analysis showing that quantum geometry removes the cosmological singularity in isotropic models, extending spacetime beyond classical limits.

Findings

Inverse scale factor operator is bounded at the singularity

Quantum evolution proceeds in discrete steps without breakdown

Spacetime extension beyond the classical singularity

Abstract

It is shown that the cosmological singularity in isotropic minisuperspaces is naturally removed by quantum geometry. Already at the kinematical level, this is indicated by the fact that the inverse scale factor is represented by a bounded operator even though the classical quantity diverges at the initial singularity. The full demonstation comes from an analysis of quantum dynamics. Because of quantum geometry, the quantum evolution occurs in discrete time steps and does not break down when the volume becomes zero. Instead, space-time can be extended to a branch preceding the classical singularity independently of the matter coupled to the model. For large volume the correct semiclassical behavior is obtained.