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

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.

28 pages, 1 figure; v2: extended discussion of singularity removal and summary

References in corpus (4)

• Spherically Symmetric Quantum Geometry: States and Basic Operators
• The Bianchi IX model in Loop Quantum Cosmology
• Quantum suppression of the generic chaotic behavior close to cosmological singularities
• The Volume Operator in Spherically Symmetric Quantum Geometry

Cited by in corpus (14)

• Anomaly freedom in perturbative loop quantum gravity
• Loop quantum cosmology and inhomogeneities
• Quantum nature of cosmological bounces
• Hamiltonian cosmological perturbation theory with loop quantum gravity corrections
• Formation and Evolution of Structure in Loop Cosmology
• Lemaitre-Tolman-Bondi collapse from the perspective of loop quantum gravity
• Quantum Cosmology: Effective Theory
• Effective constraints of loop quantum gravity
• The Dark Side of a Patchwork Universe
• The high-density regime of kinetic-dominated loop quantum cosmology
• Numerical Analysis of the Big Bounce in Loop Quantum Cosmology
• Quantum Geometry and its Implications for Black Holes
• Big Bang Singularity Resolution In Quantum Cosmology
• Factor ordering and large-volume dynamics in quantum cosmology