Publication: Hybrid quantum Gowdy cosmology: combining loop and Fock quantizations
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2008-10
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Amer Physical Soc
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Abstract
We quantize an inhomogeneous cosmological model using techniques that include polymeric quantization. More explicitly, we construct well-defined operators to represent the constraints and find the physical Hilbert space formed by their solutions, which reproduces the conventional Fock quantization for the inhomogeneities. The initial singularity is resolved in this inhomogeneous model in an extremely simple way and without imposing special boundary conditions, thus ensuring the robustness and generality of this resolution. Furthermore, this quantization constitutes a well-founded step towards the extraction of physical results and consequences from loop quantum cosmology, given the central role of the inhomogeneities in modern cosmology.
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©2008 The American Physical Society.
The authors are very grateful to J. M. Velhinho and T. Pawlowski. This work was supported by the Spanish Grants No. FIS2005-05736-C03-02 (its continuation No. FIS2008-06078-C03-03), No. FIS2006-26387-E, and No. CSD2007-00042 (CPAN); and M. M-B. by CSIC and the European Social Fund under the Grant No. I3PBPD2006.
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[1] M. Bojowald, Living Rev. Relativity 11, 4 (2008).
[2] T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, England, 2007).
[3] A. Ashtekar, M. Bojowald, and J. Lewandowski, Adv. Theor. Math. Phys. 7, 233 (2003).
[4] See, e.g., A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. Lett. 96, 141301 (2006); Phys. Rev. D 73, 124038 (2006); 74, 084003 (2006).
[5] D. W. Chiou, Phys. Rev. D 75, 024029 (2007).
[6] D. W. Chiou, Phys. Rev. D 76, 124037 (2007).
[7] K. Banerjee and G. Date, Classical Quantum Gravity 25, 145004 (2008).
[8] R. H. Gowdy, Ann. Phys. (N.Y.) 83, 203 (1974).
[9] V. Moncrief, Phys. Rev. D 23, 312 (1981).
[10] See, e.g., C. W. Misner, Phys. Rev. D 8, 3271 (1973); B. K. Berger, Ann. Phys. (N.Y.) 83, 458 (1974); Phys. Rev. D 11, 2770 (1975); Ann. Phys. (N.Y.) 156, 155 (1984); G. A. Mena Marugán, Phys. Rev. D 56, 908 (1997); M. Pierri, Int. J. Mod. Phys. D 11, 135 (2002).
[11] See, e.g., K. Kuchar, Phys. Rev. D 4, 955 (1971); A. Ashtekar and M. Pierri, J. Math. Phys. (N.Y.) 37, 6250 (1996); J. F. Barbero G., G. A. Marugán, and E. J. S. Villaseñor, Phys. Rev. D 67, 124006 (2003).
[12] A. Corichi, J. Cortez, and G. A. Mena Marugán, Phys. Rev. D 73, 041502 (2006); 73, 084020 (2006); A. Corichi, J. Cortez, G. A. Mena Marugán, and J. M. Velhinho, Classical Quantum Gravity 23, 6301 (2006); J. Cortez, G. A. Mena Marugán, and J. M. Velhinho, Phys. Rev. D 75, 084027 (2007).
[13] M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001).
[14] V. A. Belinsky, I. M. Khalatnikov, and E. M. Lifshitz, Adv. Phys. 31, 639 (1982).
[15] We will not use the Einstein summation convention.
[16] There exist different proposals to define this minimum value, which are still under discussion. This issue has been considered in [6] and by A. Ashtekar (unpublished).
[17] M. Martín-Benito, G. A. Mena Marugán, and T. Pawlowski, Phys. Rev. D 78, 064008 (2008).
[18] M. Martín-Benito, Master thesis, Universidad Complutense de Madrid, 2007.
[19] Namely, the algebraic dual of the subset of CylS of nonzero-volume states.
[20] L. J. Garay, M. Martín-Benito, G. A. Mena Marugán, and J. M. Velhinho (unpublished).