Loop quantization of vacuum Bianchi I cosmology

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 78, Issue 6, 2008, Pages

  Martin Benito M ^a   Mena Marugan G A ^a   Pawlowski, T ^a  

^a INSTITUTO DE ESTRUCTURA DE LA MATERIA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 51649126402     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.78.064008     Document Type: Article

References (41)

1. M. Bojowald, Living Rev. Relativity 1433-8351 11, 4 (2008).
2. T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, England, 2007).
3. C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, England, 2004).
4. A. Ashtekar and J. Lewandowski, Classical Quantum Gravity 21, R53 (2004). CQGRDG 0264-9381 10.1088/0264-9381/21/15/R01
5. M. Bojowald, Classical Quantum Gravity 17, 1489 (2000); CQGRDG 0264-9381 10.1088/0264-9381/17/6/312
6. M. Bojowald Classical Quantum Gravity 17, 1509 (2000); CQGRDG 0264-9381 10.1088/0264-9381/17/6/313
7. M. Bojowald Classical Quantum Gravity 18, 1055 (2001); CQGRDG 0264-9381 10.1088/0264-9381/18/6/307
8. M. Bojowald Classical Quantum Gravity 18, 1071 (2001). CQGRDG 0264-9381 10.1088/0264-9381/18/6/308
9. A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. Lett. 96, 141301 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.141301
10. A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. D 73, 124038 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.73.124038
11. A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. D 74, 084003 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.74.084003
12. W. Kamiński and J. Lewandowski, Classical Quantum Gravity 25, 035001 (2008). CQGRDG 0264-9381 10.1088/0264-9381/25/3/035001
13. A. Ashtekar, T. Pawlowski, P. Singh, and K. Vandersloot, Phys. Rev. D 75, 024035 (2007). PRVDAQ 0556-2821 10.1103/PhysRevD.75.024035
14. L. Szulc, W. Kamiński, and J. Lewandowski, Classical Quantum Gravity 24, 2621 (2007). CQGRDG 0264-9381 10.1088/0264-9381/24/10/008
15. K. Vandersloot, Phys. Rev. D 75, 023523 (2007). PRVDAQ 0556-2821 10.1103/PhysRevD.75.023523
16. E. Bentivegna and T. Pawlowski, Phys. Rev. D 77, 124025 (2008). PRVDAQ 0556-2821 10.1103/PhysRevD.77.124025
17. A. Ashtekar, M. Bojowald, and J. Lewandowski, Adv. Theor. Math. Phys. 7, 233 (2003). 1095-0761
18. A. Ashtekar and J. Pullin, Ann. Isr. Phys. Soc. AIPSDK 0309-8710 9, 65 (1990).
19. N. Manojlović and G.A. Mena Marugán, Phys. Rev. D 48, 3704 (1993). PRVDAQ 0556-2821 10.1103/PhysRevD.48.3704
20. M. Bojowald, Classical Quantum Gravity 20, 2595 (2003). CQGRDG 0264-9381 10.1088/0264-9381/20/13/310
21. D.W. Chiou, Phys. Rev. D 75, 024029 (2007). PRVDAQ 0556-2821 10.1103/PhysRevD.75.024029
22. M. Martín-Benito, Master thesis, University Complutense de Madrid, 2007.
23. M. Martín-Benito, L.J. Garay, and G.A. Mena Marugán, arXiv:0804.1098.
24. L. Szulc, arXiv:0803.3559 [Phys. Rev. D (to be published)].
25. D.W. Chiou, Phys. Rev. D 76, 124037 (2007). PRVDAQ 0556-2821 10.1103/PhysRevD.76.124037
26. These two prescriptions coincide for isotropic cosmologies. For some recent phenomenological and consistency arguments supporting the adoption of such a prescription in the isotropic case see A. Corichi and P. Singh, Phys. Rev. D 78, 024034 (2008); PRVDAQ 0556-2821 10.1103/PhysRevD.78.024034
27. W. Nelson and M. Sakellariadou, Phys. Rev. D 78, 024006 (2008). PRVDAQ 0556-2821 10.1103/PhysRevD.78.024006
28. A. Ashtekar (unpublished).
29. However, as we will see, the singularity is never crossed in the quantum evolution, contrary to the suggestions of Ref.. In addition, preliminary numerical analyses indicate that the singularity is also resolved dynamically in the physically interesting cases.
30. T. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, Berlin, 1980).
31. See, e.g., M. Reed and B. Simon, Methods of Modern Mathematical Physics I: Functional Analysis (Academic Press, San Diego, 1980).
32. For a remarkably concise exposition of the concepts and tools on functional analysis employed in this section we refer the reader to Appendix C in A. Galindo and P. Pascual, Quantum Mechanics I (Springer-Verlag, Berlin, 1990).
33. M. Martín-Benito, G.A. Mena Marugán, and T. Pawlowski (unpublished).
34. W. Kamiński (unpublished).
35. D. Marolf, arXiv:gr-qc/9508015;
36. D. Marolf Classical Quantum Gravity 12, 1199 (1995); CQGRDG 0264-9381 10.1088/0264-9381/12/5/011
37. D. Marolf Classical Quantum Gravity 12, 1441 (1995); CQGRDG 0264-9381 10.1088/0264-9381/12/6/010
38. D. Marolf Classical Quantum Gravity 12, 2469 (1995). CQGRDG 0264-9381 10.1088/0264-9381/12/10/007
39. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, and T. Thiemann, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 36, 6456 (1995). 10.1063/1.531252
40. P. Singh and K. Vandersloot, Phys. Rev. D 72, 084004 (2005). PRVDAQ 0556-2821 10.1103/PhysRevD.72.084004
41. V. Taveras, Corrections to the Friedmann Equations from LQG: Mu-Bar Framework, International Loop Quantum Gravity Seminars (Pennsylvania State University, 2008), http://relativity.phys.lsu.edu/ilqgs/taveras021908.pdf.