Loop quantum cosmology of k=1 FRW models

Dec, 2006
43 pages
Published in:
  • Phys.Rev.D 75 (2007) 024035
e-Print:
Report number:
  • IGPG-06-12-1

Citations per year

200620112016202120250102030
Abstract: (arXiv)
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.
  • 98.80.Qc
  • 04.60.Pp
  • 03.65.Sq
  • 04.60.Kz
  • quantum cosmology: loop space
  • space-time: Robertson-Walker
  • field theory: scalar
  • massless
  • big bang
  • general relativity