Built on

J. Yang, Y. Ding, Y. Ma, “Alternative quantization of the Hamiltonian in isotropic loop quantum cosmology,” [arXiv:0902.1913 [gr-qc]]
Original
1913
Earlier work this paper cites.
A. Ashtekar, M. Bojowald and L. Lewandowski, “Mathematical structure of loop quantum cosmology” Adv. Theor. Math. Phys. 7
2003
Earlier work this paper cites.
M. Bojowald, “Loop quantum cosmology”, Living Rev. Rel. 8
2005
Earlier work this paper cites.
A. Ashtekar, T. Pawlowski and P. Singh, “Quantum Nature of the Big Bang,” Phys. Rev. Lett 96
2006
Earlier work this paper cites.
A. Ashtekar, T. Pawlowski and P. Singh, “Quantum Nature of the Big Bang: An Analytical and Numerical Investigation,” Phys. Rev. D 73
2006
Earlier work this paper cites.
A. Ashtekar, T. Pawlowski and P. Singh, “Quantum nature of the big bang: Improved dynamics,” Phys. Rev. D 74
2006
Earlier work this paper cites.
A. Ashtekar and J. Lewandowski “Background independent quantum gravity: A status report,” Class. Quant. Grav. 21
2007
Earlier work this paper cites.
A. Ashtekar, T. Pawlowski, P. Singh, K. Vandersloot, “Loop quantum cosmology of k=1 FRW models,” Phys.Rev. D 75
2007
Earlier work this paper cites.

Similar

L. Szulc, W. Kaminski, J. Lewandowski, “Closed FRW model in Loop Quantum Cosmology,” Class.Quant.Grav. 24
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K. Vandersloot, “Loop quantum cosmology and the k = - 1 RW model,” Phys.Rev. D 75
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A. Corichi, T. Vukasinac and J.A. Zapata, “Polymer quantum mechanics and its continuum limit”, Phys Rev D76
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2008
Cited alongside, same era.

Then

A. Corichi and P. Singh, “Is loop quantization in cosmology unique?,” Phys. Rev. D 78
Original
2009
Later among the works it cites.
P. Singh, “Are loop quantum cosmos never singular?,” Class. Quant. Grav. 26
Original
2009
Later among the works it cites.
A. Ashtekar and E. Wilson-Ewing, “Loop quantum cosmology of Bianchi I models,” Phys. Rev. D 79
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2009
Later among the works it cites.
A. Ashtekar and E. Wilson-Ewing, “Loop quantum cosmology of Bianchi type II models,” Phys. Rev. D 80
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2009
Later among the works it cites.
W. Kaminski and T. Pawlowski, “Cosmic recall and the scattering picture of Loop Quantum Cosmology,” Phys. Rev. D 81
Original

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2011

Loop quantum cosmology of k=1 FRW: A tale of two bounces

Corichi, Alejandro, Karami, Asieh

Understand

We consider the k=1 Friedman-Robertson-Walker (FRW) model within loop quantum cosmology, paying special attention to the existence of an ambiguity in the quantization process.

In spatially non-flat anisotropic models such as Bianchi II and IX, the standard method of defining the curvature through closed holonomies is not admissible.
Instead, one has to implement the quantum constraints by approximating the connection via open holonomies.
In the case of flat k=0 FRW and Bianchi I models, these two quantization methods coincide, but in the case of the closed $k$=1 FRW model they might yield different quantum theories.

Built on

J. Yang, Y. Ding, Y. Ma, “Alternative quantization of the Hamiltonian in isotropic loop quantum cosmology,” [arXiv:0902.1913 [gr-qc]]
Original
1913
Earlier work this paper cites.
A. Ashtekar, M. Bojowald and L. Lewandowski, “Mathematical structure of loop quantum cosmology” Adv. Theor. Math. Phys. 7
2003
Earlier work this paper cites.
M. Bojowald, “Loop quantum cosmology”, Living Rev. Rel. 8
2005
Earlier work this paper cites.
A. Ashtekar, T. Pawlowski and P. Singh, “Quantum Nature of the Big Bang,” Phys. Rev. Lett 96
2006
Earlier work this paper cites.
A. Ashtekar, T. Pawlowski and P. Singh, “Quantum Nature of the Big Bang: An Analytical and Numerical Investigation,” Phys. Rev. D 73
2006
Earlier work this paper cites.
A. Ashtekar, T. Pawlowski and P. Singh, “Quantum nature of the big bang: Improved dynamics,” Phys. Rev. D 74
2006
Earlier work this paper cites.
A. Ashtekar and J. Lewandowski “Background independent quantum gravity: A status report,” Class. Quant. Grav. 21
2007
Earlier work this paper cites.
A. Ashtekar, T. Pawlowski, P. Singh, K. Vandersloot, “Loop quantum cosmology of k=1 FRW models,” Phys.Rev. D 75
2007
Earlier work this paper cites.