Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-10-22
Phys.Rev.D80:103507,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
8 pages, 7 figures, accepted for publication in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.80.103507
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 Schr\"{o}dinger 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.
Amemiya Fumitoshi
Koike Tatsuhiko
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