Open FRW model in Loop Quantum Cosmology

Abstract

Open FRW model in Loop Quantum Cosmology is under consideration. The left and right invariant vector fields and holonomies along them are studied. It is shown that in the hyperbolic geometry of $k=-1$ it is possible to construct a suitable loop which provides us with quantum scalar constraint originally introduced by Vandersloot. The quantum scalar constraint operator with negative cosmological constant is proved to be essentially self-adjoint.

12 pages, no figures, latex

References in corpus (16)

• Background Independent Quantum Gravity: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Theory of Gravity I: Area Operators
• Quantum Nature of the Big Bang
• Absence of Singularity in Loop Quantum Cosmology
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop Quantum Cosmology
• Introduction to Modern Canonical Quantum General Relativity
• Loop quantum cosmology of k=1 FRW models
• Isotropic Loop Quantum Cosmology
• Loop quantum cosmology and the k = - 1 RW model
• Closed FRW model in Loop Quantum Cosmology
• Loop Quantum Cosmology I: Kinematics
• Loop Quantum Cosmology, Boundary Proposals, and Inflation
• Loop Quantum Cosmology II: Volume Operators
• Loop Quantum Cosmology III: Wheeler-DeWitt Operators

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• Finite-time Cosmological Singularities and the Possible Fate of the Universe
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• Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
• Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes
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• Loop Quantum Cosmology: Physics of Singularity Resolution and its Implications
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