Degenerate Configurations, Singularities and the Non-Abelian Nature of Loop Quantum Gravity

TL;DR

This paper examines the role of degenerate configurations and singularities in loop quantum gravity, emphasizing the importance of dynamical evolution and non-Abelian effects in understanding singularity resolution.

Contribution

It provides a critical analysis of degenerate configurations in loop quantum gravity, highlighting the influence of non-Abelian effects and connecting insights from loop quantum cosmology.

Findings

Loop quantum cosmology's mechanism is unaffected by unbounded inverse volume behavior.

Non-Abelian effects contribute to unboundedness, independent of inhomogeneities.

Dynamical considerations are crucial for interpreting degenerate configurations.

Abstract

Degenerate geometrical configurations in quantum gravity are important to understand if the fate of classical singularities is to be revealed. However, not all degenerate configurations arise on an equal footing, and one must take into account dynamical aspects when interpreting results: While there are many degenerate spatial metrics, not all of them are approached along the dynamical evolution of general relativity or a candidate theory for quantum gravity. For loop quantum gravity, relevant properties and steps in an analysis are summarized and evaluated critically with the currently available information, also elucidating the role of degrees of freedom captured in the sector provided by loop quantum cosmology. This allows an outlook on how singularity removal might be analyzed in a general setting and also in the full theory. The general mechanism of loop quantum cosmology will be shown to be insensitive to recently observed unbounded behavior of inverse volume in the full theory. Moreover, significant features of this unboundedness are not a consequence of inhomogeneities but of non-Abelian effects which can also be included in homogeneous models.