Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes

TL;DR

This paper demonstrates that in loop quantum Bianchi-IX spacetimes, all classical strong singularities are resolved or replaced by weak singularities, ensuring geodesic completeness in effective quantum models.

Contribution

It compares two quantization methods in loop quantum cosmology and shows that all classical strong singularities are avoided, with conditions for bounded physical scalars.

Findings

All strong singularities are resolved in the effective quantum spacetime.

Both quantizations result in bounded energy density, expansion, and shear scalars.

Potential curvature divergences are weak and do not break geodesic extension.

Abstract

We study the generic resolution of strong singularities in loop quantized effective Bianchi-IX spacetime in two different quantizations - the connection operator based `A' quantization and the extrinsic curvature based `K' quantization. We show that in the effective spacetime description with arbitrary matter content, it is necessary to include inverse triad corrections to resolve all the strong singularities in the `A' quantization. Whereas in the `K' quantization these results can be obtained without including inverse triad corrections. Under these conditions, the energy density, expansion and shear scalars for both of the quantization prescriptions are bounded. Notably, both the quantizations can result in potentially curvature divergent events if matter content allows divergences in the partial derivatives of the energy density with respect to the triad variables at a finite energy density. Such events are found to be weak curvature singularities beyond which geodesics can be extended in the effective spacetime. Our results show that all potential strong curvature singularities of the classical theory are forbidden in Bianchi-IX spacetime in loop quantum cosmology and geodesic evolution never breaks down for such events.