Loop quantum cosmology of k=1 FRW models

Abhay Ashtekar, Tomasz Pawlowski, Parampreet Singh, and Kevin Vandersloot
Phys. Rev. D 75, 024035 – Published 26 January 2007

Abstract

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 semiclassical 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.

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  • Received 18 December 2006

DOI:https://doi.org/10.1103/PhysRevD.75.024035

©2007 American Physical Society

Authors & Affiliations

Abhay Ashtekar1,2,*, Tomasz Pawlowski1,†, Parampreet Singh1,‡, and Kevin Vandersloot1,3,§

  • 1Institute for Gravitational Physics and Geometry, Physics Department, Penn State, University Park, Pennsylvania 16802, USA
  • 2Institute for Theoretical Physics, University of Utrecht, Princetonplein 5, 3584 CC Utrecht, The Netherlands
  • 3Institute of Cosmology and Gravitation, Mercantile House, Portsmouth University, Portsmouth PO1 2EG, United Kingdom

  • *Electronic address: ashtekar@gravity.psu.edu
  • Electronic address: pawlowsk@gravity.psu.edu
  • Electronic address: singh@gravity.psu.edu
  • §Electronic address: Kevin.Vandersloot@port.ac.uk

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Vol. 75, Iss. 2 — 15 January 2007

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