Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-12-18
Phys.Rev.D75:024035,2007
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Typos corrected. To appear in Physical Review D
Scientific paper
10.1103/PhysRevD.75.024035
The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semi-classical at some late time, the big-bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the `difficulties' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists.
Ashtekar Abhay
Pawlowski Tomasz
Singh Parampreet
Vandersloot Kevin
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