Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes

TL;DR

This paper investigates how loop quantum gravity methods resolve singularities in Bianchi-II spacetimes, showing that certain quantizations lead to geodesically complete, non-singular models, extending previous results to more complex anisotropic universes.

Contribution

It compares two loop quantum Bianchi-II quantizations, demonstrating that extrinsic curvature based quantization naturally resolves all strong singularities without additional conditions.

Findings

Extrinsic curvature quantization resolves all strong singularities.

Connection based quantization requires inverse triad modifications or energy conditions.

Both approaches can still have weak curvature singularities from pressure divergences.

Abstract

Generic resolution of singularities and geodesic completeness in the loop quantization of Bianchi-II spacetimes with arbitrary minimally coupled matter is investigated. Using the effective Hamiltonian approach, we examine two available quantizations: one based on the connection operator and second by treating extrinsic curvature as connection via gauge fixing. It turns out that for the connection based quantization, either the inverse triad modifications or imposition of weak energy condition is necessary to obtain a resolution of all strong singularities and geodesic completeness. In contrast, the extrinsic curvature based quantization generically resolves all strong curvature singularities and results in a geodesically complete effective spacetime without inverse triad modifications or energy conditions. In both the quantizations, weak curvature singularities can occur resulting from divergences in pressure and its derivatives at finite densities. These are harmless events beyond which geodesics can be extended. Our work generalizes previous results on the generic resolution of strong singularities in the loop quantization of isotropic, Bianchi-I and Kantowski-Sachs spacetimes.