## Publication: Inhomogeneous loop quantum cosmology: hybrid quantization of the Gowdy model

Loading...

##### Official URL

##### Full text at PDC

##### Publication Date

2010-08-30

##### Authors

##### Advisors (or tutors)

##### Editors

##### Journal Title

##### Journal ISSN

##### Volume Title

##### Publisher

Amer Physical Soc

##### Abstract

The Gowdy cosmologies provide a suitable arena to further develop loop quantum cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of linearly polarized gravitational waves, we detail a hybrid quantum theory in which we combine a loop quantization of the degrees of freedom that parametrize the subfamily of homogeneous solutions, which represent Bianchi I spacetimes, and a Fock quantization of the inhomogeneities. Two different theories are constructed and compared, corresponding to two different schemes for the quantization of the Bianchi I model within the improved dynamics formalism of loop quantum cosmology. One of these schemes has been recently put forward by Ashtekar and Wilson-Ewing. We address several issues, including the quantum resolution of the cosmological singularity, the structure of the superselection sectors in the quantum system, or the construction of the Hilbert space of physical states.

##### Description

© 2010 The American Physical Society.
The authors are grateful to D. Brizuela, D. Martín de Blas, H. Sahlmann, J. Olmedo, T. Pawlowski, E. Wilson-Ewing, and especially to J. M. Velhinho, for useful discussions. This work was supported by the Spanish MICINN under Project No. FIS2008-06078-C03-03 and the Consolider-Ingenio 2010 Program CPAN under Contract No. CSD2007-00042. M. M-B. is supported by CSIC and the European Social Fund under Grant No. I3PBPD2006.

##### UCM subjects

##### Unesco subjects

##### Keywords

##### Citation

[1] T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, England, 2007); C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, England, 2004); A. Ashtekar and J. Lewandowski, Classical Quantum Gravity 21, R53 (2004).
[2] M. Bojowald, Living Rev. Relativity 11, 4 (2008).
[3] A. Ashtekar, M. Bojowald, and J. Lewandowski, Adv. Theor. Math. Phys. 7, 233 (2003).
[4] A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. D 74, 084003 (2006).
[5] M. Martı´n-Benito, G. A. Mena Marugán, and J. Olmedo, Phys. Rev. D 80, 104015 (2009).
[6] A. Ashtekar, T. Pawlowski, P. Singh, and K. Vandersloot, Phys. Rev. D 75, 024035 (2007).
[7] L. Szulc, W. Kaminski, and J. Lewandowski, Classical Quantum Gravity 24, 2621 (2007); K. Vandersloot, Phys. Rev. D 75, 023523 (2007).
[8] E. Bentivegna and T. Pawlowski, Phys. Rev. D 77, 124025 (2008).
[9] D. W. Chiou, Phys. Rev. D 75, 024029 (2007).
[10] D. W. Chiou, Phys. Rev. D 76, 124037 (2007).
[11] M. Martín-Benito, G. A. Mena Marugán, and T. Pawlowski, Phys. Rev. D 78, 064008 (2008).
[12] A. Ashtekar and E. Wilson-Ewing, Phys. Rev. D 79, 083535 (2009).
[13] A. Ashtekar and E. Wilson-Ewing, Phys. Rev. D 80, 123532 (2009).
[14] R. H. Gowdy, Ann. Phys. (N.Y.) 83, 203 (1974).
[15] V. Moncrief, Phys. Rev. D 23, 312 (1981).
[16] J. Isenberg and V. Moncrief, Ann. Phys. (N.Y.) 199, 84 (1990).
[17] 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).
[18] A. Corichi, J. Cortez, and G. A. Mena Maruga´n, Phys. Rev. D 73, 041502 (2006); 73, 084020 (2006).
[19] 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).
[20] M. Martín-Benito, L. J. Garay, and G. A. Mena Maruga´n, Phys. Rev. D 78, 083516 (2008).
[21] G. A. Mena Maruga´n and M. Martı´n-Benito, Int. J. Mod. Phys. A 24, 2820 (2009).
[22] G. A. Mena Marugán and M. Montejo, Phys. Rev. D 58, 104017 (1998).
[23] Here, we call physical area that measured by the area operator defined on the kinematical Hilbert space, to distinguish it from the fiducial area.
[24] There is a discrepancy in signs between this representation and that of Ref. [12] because, in the latter, is considered to change sign under internal parity transformations, namely, ¼ j jsgnðvÞ, while we treat just as a positive free parameter, which therefore is unaffected by transformations of the dynamical variables.
[25] We understand the nondensitized Hamiltonian constraint as referring to the scalar constraint with the same densitization as in LQG.
[26] This difference is due to the factor 1=ð16 GÞ accompanying the classical action, which is not included in the definition of the constraint in this paper.
[27] D. Marolf, arXiv:gr-qc/9508015; Classical Quantum Gravity 12, 1199 (1995); 12, 1441 (1995); 12, 2469 (1995).
[28] A. D. Rendall, Classical Quantum Gravity 10, 2261 (1993); arXiv:gr-qc/9403001.
[29] D. Brizuela, G. A. Mena Maruga´n, and T. Pawlowski, Classical Quantum Gravity 27, 052001 (2010).
[30] Nonetheless, we note that dffiffiffiffi V p ðF^ i F^ jÞ dffiffiffiffi V p is still a constant of motion. We thank T. Pawlowski for pointing out this fact.
[31] M. Martín-Benito, G. A. Mena Marugán, and E. WilsonEwing, arXiv:1006.2369.
[32] G. A. Mena Maruga´n, T. Pawlowski, and E. Wilson-Ewing "An Effective Analysis of the Hybrid Quantization of the Gowdy Model" (unpublished).