Gauge-invariant construction of quantum cosmology

Abstract

We present and analyze a gauge-invariant quantum theory of the Friedmann-Robertson-Walker universe with dust. We construct the reduced phase space spanned by gauge-invariant quantities by using the so-called relational formalism at the classical level. The reduced phase space thereby obtained can be quantized in the same manner as an ordinary mechanical system. We carry out the quantization and obtain the Schrödinger equation. This quantization procedure realizes a possible resolution to the problem of time and observables in canonical quantum gravity. We analyze the classical initial singularity of the theory by evolving a wave packet backward in time and evaluating the expectation value of the scale factor. It is shown that the initial singularity of the Universe is avoided by the quantum gravitational effects.

8 pages, 7 figures, accepted for publication in Phys. Rev. D

References in corpus (6)

• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Partial observables
• Partial and Complete Observables for Hamiltonian Constrained Systems
• Quantum cosmological perfect fluid models
• Reduced Phase Space Quantization and Dirac Observables
• Dynamical Vacuum in Quantum Cosmology

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• Infrared signatures of quantum bounce in a minisuperspace analysis of Lema\^ıtre-Tolman-Bondi dust collapse
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• Analyzing quantum gravity spillover in the semiclassical regime
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• Bouncing and Cyclic Quantum Primordial Universes and the Ordering Problem
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• Quantum cosmology in teleparallel gravity with a boundary term