Effective equations for isotropic quantum cosmology including matter

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 76, Issue 6, 2007, Pages

  Bojowald, Martin ^a   Hernández, Hector ^b   Skirzewski, Aureliano ^c  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b UNIVERSIDAD AUTÓNOMA DE CHIHUAHUA   (Mexico)

^c UNIVERSIDAD DE LOS ANDES   (Venezuela)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 34848916982     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.76.063511     Document Type: Article

References (37)

1. P.J. Steinhardt and N. Turok, Phys. Rev. D 65, 126003 (2002). PRVDAQ 0556-2821 10.1103/PhysRevD.65.126003
2. G.F.R. Ellis and R. Maartens, Classical Quantum Gravity CQGRDG 0264-9381 21, 223 (2004). 10.1088/0264-9381/21/1/015
3. J.E. Lidsey, D.J. Mulryne, N.J. Nunes, and R. Tavakol, Phys. Rev. D 70, 063521 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.70.063521
4. M. Bojowald, R. Maartens, and P. Singh, Phys. Rev. D 70, 083517 (2004). PRVDAQ 0556-2821 10.1103/PhysRevD.70.083517
5. D.J. Mulryne, R. Tavakol, J.E. Lidsey, and G.F.R. Ellis, Phys. Rev. D 71, 123512 (2005). PRVDAQ 0556-2821 10.1103/PhysRevD.71.123512
6. P. Singh, K. Vandersloot, and G.V. Vereshchagin, Phys. Rev. D 74, 043510 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.74.043510
7. M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001). PRLTAO 0031-9007 10.1103/PhysRevLett.86.5227
8. M. Bojowald, Phys. Rev. Lett. 95, 061301 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.061301
9. M. Bojowald, AIP Conf. Proc. APCPCS 0094-243X 910, 294 (2007). 10.1063/1.2752483
10. A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. Lett. 96, 141301 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.141301
11. A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. D 73, 124038 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.73.124038
12. A. Ashtekar, T. Pawlowski, and P. Singh, Phys. Rev. D 74, 084003 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.74.084003
13. M. Bojowald, Phys. Rev. D 75, 081301(R) (2007). PRVDAQ 0556-2821
14. M. Bojowald, Phys. Rev. D 75, 123512 (2007). PRVDAQ 0556-2821 10.1103/PhysRevD.75.123512
15. Solvability requires one to drop some of the ingredients of a loop quantized Hamiltonian which, however, are not relevant for states of a universe with large matter content. The solvable model is thus not exactly the same as a loop quantization or that used in the numerical studies of but still allows one to analyze the bounce. Note that also in the dynamical equation was adapted for the numerical purposes and differs from what one would obtain in a loop quantization. None of these changes matter for properties of the bounce of a large universe.
16. M. Bojowald and A. Skirzewski, Rev. Math. Phys. 18, 713 (2006). RMPHEX 0129-055X 10.1142/S0129055X06002772
17. A. Skirzewski, Ph.D. thesis, Humboldt-Universität Berlin, 2006.
18. M. Bojowald and A. Skirzewski, Int. J. Geom. Methods Mod. Phys. 4, 25 (2007). 0219-8878 10.1142/S0219887807001941
19. M. Bojowald, H. Hernández, M. Kagan, and A. Skirzewski, Phys. Rev. D 75, 064022 (2007). PRVDAQ 0556-2821 10.1103/PhysRevD.75.064022
20. M. Bojowald, Classical Quantum Gravity CQGRDG 0264-9381 19, 2717 (2002). 10.1088/0264-9381/19/10/313
21. A. Ashtekar, M. Bojowald, and J. Lewandowski, Adv. Theor. Math. Phys. 7, 233 (2003). 1095-0761
22. As written, this refers to exponentials depending only on connection components while recent investigations of loop quantum cosmology have suggested the use of triad dependent holonomies, i.e. α(p) in eiαc, in Hamiltonian constraint operators. While basic holonomies in the holonomy-flux algebra do not depend on triad components, the appearance of triad dependent holonomies can be motivated by lattice refinements of an inhomogeneous state occurring in a physical state. Our following discussion of the qualitative behavior does not depend much on which form of holonomies is used in the constraint since alternative cases can be mapped into each other by canonical transformations of (p,J) before quantization.
23. M. Bojowald, Classical Quantum Gravity CQGRDG 0264-9381 18, 1071 (2001). 10.1088/0264-9381/18/6/308
24. M. Bojowald and F. Hinterleitner, Phys. Rev. D 66, 104003 (2002). PRVDAQ 0556-2821 10.1103/PhysRevD.66.104003
25. F. Hinterleitner and S. Major, Phys. Rev. D 68, 124023 (2003). PRVDAQ 0556-2821 10.1103/PhysRevD.68.124023
26. X. Jaén, J. Llosa, and A. Molina, Phys. Rev. D 34, 2302 (1986). PRVDAQ 0556-2821 10.1103/PhysRevD.34.2302
27. J.Z. Simon, Phys. Rev. D 41, 3720 (1990). PRVDAQ 0556-2821 10.1103/PhysRevD.41.3720
28. M. Bojowald, Nature Phys. 3, 523 (2007). 1745-2481 10.1038/nphys654
29. P. Singh, Phys. Rev. D 73, 063508 (2006). PRVDAQ 0556-2821 10.1103/PhysRevD.73.063508
30. D. Samart and B. Gumjudpai, arXiv:0704.3414 [Phys. Rev. D (to be published)]. PRVDAQ 0556-2821
31. X. Zhang and Y. Ling, arXiv:0705.2656 [J. Cosmol. Astropart. Phys. 1475-7516 (to be published)].
32. H. Wei and S.N. Zhang, arXiv:0705.4002 [Phys. Rev. D (to be published)]. PRVDAQ 0556-2821
33. M. Szydłowski, W. Godłowski, and T. Stachowiak, arXiv:0706.0283.
34. M. Bojowald, Phys. Rev. Lett. 89, 261301 (2002). PRLTAO 0031-9007 10.1103/PhysRevLett.89.261301
35. M. Bojowald, Living Rev. Relativity 8, 11 (2005), http://relativity. livingreviews.org/Articles/lrr-2005-11/. 1433-8351
36. M. Bojowald, Gen. Relativ. Gravit. GRGVA8 0001-7701 38, 1771 (2006). 10.1007/s10714-006-0348-4
37. M. Bojowald, D. Cartin, and G. Khanna, Phys. Rev. D 76, 064018 (2007). PRVDAQ 0556-2821 10.1103/PhysRevD.76.064018