Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime

TL;DR

This paper demonstrates that in loop quantum Kantowski-Sachs spacetime, strong singularities are resolved and the effective spacetime remains geodesically complete, despite potential weak singularities under exotic conditions.

Contribution

It extends the understanding of singularity resolution in loop quantum cosmology to the Kantowski-Sachs model, showing generic resolution of strong singularities.

Findings

Strong singularities are resolved for arbitrary matter.

Curvature invariants remain finite in typical evolution.

Effective spacetime is geodesically complete.

Abstract

Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that even though expansion and shear scalars are universally bounded, there can exist events where curvature invariants can diverge. However, such events can occur only for very exotic equations of state when pressure or derivatives of energy density with respect to triads become infinite at a finite energy density. In all other cases curvature invariants are proved to remain finite for any evolution in finite proper time. We find the novel result that all strong singularities are resolved for arbitrary matter. Weak singularities pertaining to above potential curvature divergence events can exist. The effective spacetime is found to be geodesically complete for particle and null geodesics in finite time evolution. Our results add to a growing evidence for generic resolution of strong singularities using effective dynamics in loop quantum cosmology by generalizing earlier results on isotropic and Bianchi-I spacetimes.