### 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.

Original language | English (US) |
---|---|

Article number | 024035 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 75 |

Issue number | 2 |

DOIs | |

State | Published - Jan 31 2007 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

### Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*75*(2), [024035]. https://doi.org/10.1103/PhysRevD.75.024035

}

*Physical Review D - Particles, Fields, Gravitation and Cosmology*, vol. 75, no. 2, 024035. https://doi.org/10.1103/PhysRevD.75.024035

**Loop quantum cosmology of k=1 FRW models.** / Ashtekar, Abhay; Pawlowski, Tomasz; Singh, Parampreet; Vandersloot, Kevin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Loop quantum cosmology of k=1 FRW models

AU - Ashtekar, Abhay

AU - Pawlowski, Tomasz

AU - Singh, Parampreet

AU - Vandersloot, Kevin

PY - 2007/1/31

Y1 - 2007/1/31

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33846502204&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846502204&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.75.024035

DO - 10.1103/PhysRevD.75.024035

M3 - Article

AN - SCOPUS:33846502204

VL - 75

JO - Physical Review D

JF - Physical Review D

SN - 0556-2821

IS - 2

M1 - 024035

ER -