Loop quantum cosmology: An overview

General Relativity and Gravitation

Volumn 41, Issue 4, 2009, Pages 707-741

  Ashtekar, Abhay ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Loop quantum cosmology; Planck scale physics; Quantum geometry; Singularity resolution

Indexed keywords

EID: 63349109219     PISSN: 00017701     EISSN: 15729532     Source Type: Journal    
DOI: 10.1007/s10714-009-0763-4     Document Type: Article

References (70)

1. Wheeler J.A.: Superspace and quantum geometrodynamics. In: Wheeler, J.A., DeWitt, C.M. (eds) Battelle Rencontres., Benjamin, New York (1972)
2. Misner, C.W.: Mixmaster universe. Phys. Rev. Lett. 22, 1071-1074 (1969); Minisuperspace. In: Magic without Magic: John Archibald Wheeler; a collection of essays in honor of his sixtieth birthday. W. H. Freeman, San Francisco (1972)
3. M. Bojowald 2005 Loop quantum cosmology Liv. Rev. Rel. 8 11
4. A. Ashtekar 2007 An introduction to loop quantum gravity through cosmology Nuovo Cimento 112 1 20 arXiv:gr-qc/0702030
5. A. Ashtekar J. Lewandowski 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53 R152
6. Rovelli C.: Quantum Gravity. Cambridge University Press, Cambridge (2004)
7. Thiemann T.: Introduction to Modern Canonical Quantum General Relativity. Cambridge University Press, Cambridge (2007)
8. A. Ashtekar J. Lewandowski D. Marolf T. Mourão J. Thiemann 1995 Quantization of diffeomorphism invariant theories of connections with local degrees of freedom J. Math. Phys. 36 6456 6493
9. Rovelli, R., Smolin, L.: Discreteness of area and volume in quantum gravity. Nucl. Phys. B 442, 593-622 (1995); Erratum B 456, 753 (1996)
10. A. Ashtekar J. Lewandowski 1997 Quantum theory of geometry I: area operators Class. Quantum Grav. 14 A55 A81
11. A. Ashtekar J. Lewandowski 1997 Quantum theory of geometry II: volume operators Adv. Theo. Math. Phys. 1 388 429
12. J.B. Hartle S.W. Hawking 1983 Wave function of the Universe Phys. Rev. D 28 2960
13. M. Gasperini G. Veneziano 2003 The pre-big bang scenario in string cosmology Phys. Rept. 373 1
14. J. Khoury B.A. Ovrut P.J. Steinhardt N. Turok 2001 The ekpyrotic Universe: colliding branes and the origin of the hot big bang Phys. Rev. D 64 123522
15. J. Khoury B. Ovrut N. Seiberg P.J. Steinhardt N. Turok 2002 From big crunch to big bang Phys. Rev. D 65 086007
16. Ashtekar, A., Stachel, J. (eds): Conceptual problems of quantum gravity. Birkhäuser, Boston (1988)
17. Komar A.: Quantization program for general relativity. In: Carmeli, M., Fickler, S.I., Witten, L. (eds) Relativity, Plenum, New York (1970)
18. Kuchar K.: Canonical methods of quantization. In: Isham, C.J., Penrose, R., Sciama, D.W. (eds) Quantum Gravity 2, A Second Oxford Symposium, Clarendon Press, Oxford (1981)
19. B.S. DeWitt 1967 Quantum theory of gravity I. The canonical theory Phys. Rev. 160 1113 1148
20. D. Green W. Unruh 2004 Difficulties with recollapsing models in closed isotropic loop quantum cosmology Phys. Rev. D 70 103502 arXiv:gr-qc/04-0074
21. A. Ashtekar T. Pawlowski P. Singh 2006 Quantum nature of the big bang: an analytical and numerical investigation I Phys. Rev. D 73 124038
22. Ashtekar, A., Pawlowski, T., Singh, P.: Loop quantum cosmology in the pre-inflationary epoch (in preparation)
23. C. Rovelli 1990 Quantum mechanics without time: a model Phys. Rev. 42 2638
24. A. Ashtekar T. Pawlowski P. Singh 2006 Quantum nature of the big bang: improved dynamics Phys. Rev. D 74 084003
25. C. Kiefer 1988 Wavepsckets in minisuperspace Phys. Rev. D 38 1761 1772
26. Marolf, D.: Refined algebraic quantization: Systems with a single constraint. arXive:gr-qc/9508015
27. D. Marolf 1994 Quantum observables and recollapsing dynamics Class. Quantum Grav. 12 1199 1220
28. A. Ashtekar L. Bombelli A. Corichi 2005 Semiclassical states for constrained systems Phys. Rev. D 72 025008
29. A. Kamenshchik C. Kiefer B. Sandhofer 2007 Quantum cosmology with big break singularity Phys. Rev. D 76 064032
30. A. Ashtekar T. Pawlowski P. Singh K. Vandersloot 2006 Loop quantum cosmology of k = 1 FRW models Phys. Rev. D 75 0240035
31. L. Szulc W. Kaminski J. Lewandowski 2006 Closed FRW model in loop quantum cosmology Class. Quantum Grav. 24 2621 2635
32. M. Bojowald 2001 Absence of singularity in loop quantum cosmology Phys. Rev. Lett. 86 5227 5230
33. A. Ashtekar M. Bojowald J. Lewandowski 2003 Mathematical structure of loop quantum cosmology Adv. Theo. Math. Phys. 7 233 268
34. J. Lewandowski A. Okolow H. Sahlmann T. Thiemann 2006 Uniqueness of diffeomorphism invariant states on holonomy flux algebras Comm. Math. Phys. 267 703 733
35. C. Fleishchack 2009 Representations of the Weyl algebra in quantum geometry Comm. Math. Phys. 235 67 140
36. J. Brunnemann T. Thiemann 2006 On (cosmological) singularity avoidance in loop quantum gravity Class. Quantum Grav. 23 1395 1428
37. A. Ashtekar T. Pawlowski P. Singh 2006 Quantum nature of the big bang Phys. Rev. Lett. 96 141301
38. A. Corichi P. Singh 2008 Is loop quantization in cosmology unique? Phys. Rev. D 78 024034
39. E. Bentivegna T. Pawlowski 2008 Anti-deSitter universe dynamics in LQC Phys. Rev. D 77 124025
40. Ashtekar, A., Pawlowski, T.: Loop quantum cosmology with a positive cosmological constant (in preparation)
41. Ashtekar, A., Wilson-Ewing, E.: Loop quantum cosmology of Binachi I models (in preparation)
42. W. Kamin'ski J. Lewandowski l. Szulc 2008 The status of quantum geometry in the dynamical sector of loop quantum cosmology, Class Quantum Grav. 25 055003
43. Kamin'ski, W., Lewandowski, J.: The flat FRW model in LQC: the self-adjointness, arXiv:0709.3120
44. M. Martin-Benito L.J. Garay G.A. Mena Marugan 2008 Hybrid quantum 7Gowdy cosmology: combining loop and Fock quantizations Phys. Rev. D 78 083516
45. Copeland, E.J., Mulryne, D.J., Nunes, N.J., Shaeri, M.: The gravitational wave background from super-inflation in Loop Quantum Cosmology, arXiv:0810.0104
46. Copeland, E.J., Mulryne, D.J., Nunes, N.J., Shaeri, M.: Superinflation in loop quantum cosmology, Phys. Rev. D 77, 023510 (2008) Research highlights in Nature: Roll with it: http://www.nature.com/nphys/journal/v4/n3/full/nphys900. html
47. L. Parisi M. Bruni R. Maartens K. Vandersloot 2007 The Einstein static universe in loop quantum cosmology Class. Quantum Grav. 24 6243 6254
48. X. Zhang Y. Ling 2007 Inflationary universe in loop quantum cosmology JCAP 0708 012
49. Xu, P., Zhang, S.N.: Cosmological evolution of interacting phantom (quintessence) model in Loop Quantum Gravity, JCAP06, 007 (2008)
50. X. Fu H. Yu P. Wu 2008 Dynamics of interacting phantom scalar field dark energy in loop quantum cosmology Phys. Rev. D 78 063001
51. Willis, J.: On the low energy ramifications and a mathematical extension of loop quantum gravity. Ph.D. Dissertation, The Pennsylvaina State University (2004)
52. Ashtekar, A., Bojowald, M., Willis, J.: Corrections to Friedmann equations induced by quantum geometry, IGPG preprint (2004)
53. V. Taveras 2008 LQC corrections to the Friedmann equations for a universe with a free scalar field Phys. Rev. D 78 064072
54. D.W. Chiou K. Vandersloot 2007 Behavior of non-linear anisopropies in bouncing Bianchi I models of loop quantum cosmology Phys. Rev. D 76 084015
55. M. Bojowald 2007 Dynamical coherent states and physical solutions of quantum cosmological bounces Phys. Rev. D 75 123512
56. A. Ashtekar A. Corichi P. Singh 2008 Robustness of predictions of loop quantum cosmology Phys. Rev. D 77 024046
57. Ashtekar A., Schilling T.A.: Geometrical formulation of quantum mechanics. In: Harvey, A. (eds) Einstein's Path: Essays in Honor of Engelbert Schücking, pp. 23-65. Springer, New York (1999) arXiv:gr-qc/9706069
58. A. Borde A. Guth A. Vilenkin 2003 Inflationary spacetimes are not past-complete Phys. Rev. Lett. 90 151301
59. Singh, P.: Are loop quantum cosmologies never singular? arXiv:0901.2750
60. Rendall A.D.: The nature of spacetime singularities. In: Ashtekar, A. (eds) 100 Years of Relativity-Space-Time Structure: Einstein and Beyond, World Scientific, Singapore (2005) arXiv:gr-qc/0503112
61. Ashtekar, A., Henderson, A., Sloan, D.: Hamiltonian formulation of general relativity and the Belinksii, Khalatnikov, Lifshitz conjecture, arXiv:0811.4160
62. R. Bousso 1999 A covariant entropy conjecture JHEP 07 004
63. E.E. Flanagan D. Marolf R.M. Wald 2000 Proof of the classical versions of the Bousso entropy bound and of the Generalized Second Law Phys. Rev. D 62 084035
64. R. Bousso E.E. Flanagan D. Marolf 2003 Simple sufficient conditions for the generalized covariant entropy bound Phys. Rev. D 68 64001 arXiv:hep-th/0305149
65. A. Ashtekar E. Wilson-Ewing 2008 The covariant entropy bound and loop quantum cosmology Phys. Rev. D 8 06407
66. J.M. Velhinho 2004 on the kinematical structure of loop quantum cosmology Class. Quantum Grav. 21 L109
67. Giesel, K., Hofmann, S., Thiemann, T., Winkler, O.: Manifestly Gauge-Invariant General Relativistic Perturbation Theory: I. Foundations, arXiv:0711.0115
68. Manifestly Gauge-Invariant General Relativistic Perturbation Theory: II. FRW Background and First Order, arXiv:0711.0117
69. D. Brown K. Kuchař 1995 Dust as a standard of space and time in canonical quantum gravity Phys. Rev. D 51 5600 5629
70. Varadarajan, M.: On the resolution of the big bang singularity in the isotropic loop quantum cosmology, arXiv:0812.0272