A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology

Abstract

We re-examine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.

17 pages, no figures. Typos corrected. Minor changes. Version to be published in PRD

References in corpus (19)

• Quantum Nature of the Big Bang: Improved dynamics
• Loop quantum cosmology of k=1 FRW models
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Are loop quantum cosmos never singular?
• Loop Quantum Cosmology: An Overview
• Loop quantum cosmology and the k = - 1 RW model
• Closed FRW model in Loop Quantum Cosmology
• Anti-deSitter universe dynamics in LQC
• Is loop quantization in cosmology unique?
• Loop quantum cosmology and inhomogeneities
• Loop Quantization of Vacuum Bianchi I Cosmology
• Lattice refining loop quantum cosmology, anisotropic models and stability
• Loop Quantum Cosmology in Bianchi Type I Models: Analytical Investigation
• Quantum bounce and cosmic recall
• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
• The flat FRW model in LQC: the self-adjointness
• Physical time and other conceptual issues of QG on the example of LQC

Cited by in corpus (1)

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