Stepping out of homogeneity in loop quantum cosmology

Classical and Quantum Gravity

Volumn 25, Issue 22, 2008, Pages

  Rovelli, Carlo ^a,c   Vidotto, Francesca ^a,b,c  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b UNIVERSITY OF PADOVA   (Italy)

^c CNRS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 62549165883     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/25/22/225024     Document Type: Article

References (69)

1. Ashtekar A, Bojowald M and Lewandowski J 2003 Mathematical structure of loop quantum cosmology Adv. Theor. Math. Phys. 7 233-68
2. Ashtekar A, Pawlowski T and Singh P 2006 Quantum nature of the big bang arXiv:gr-qc/0602086v2
3. Ashtekar A, Corichi A and Singh P 2007 Robustness of key features of loop quantum cosmology arXiv:0710.3565
4. Ashtekar A 2007 An introduction to loop quantum gravity through cosmology arXiv:gr-qc/0702030
5. Bojowald M 2002 Isotropic loop quantum cosmology Class. Quantum Grav. 19 2717-42
6. Bojowald M 2005 Loop quantum cosmology Living Rev. Rel. 8 11
7. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
8. Ashtekar A and Lewandowski J 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53
9. Thiemann T 2007 Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press)
10. Rovelli C and Smolin L 1988 Knot theory and quantum gravity Phys. Rev. Lett. 61 1155-8
11. Rovelli C and Smolin L 1990 Loop space representation for quantum general relativity Nucl. Phys. B 331 80-152
12. Ashtekar A, Rovelli C and Smolin L 1992 Weaving a classical geometry with quantum threads Phys. Rev. Lett 69 237
13. Rovelli C and Smolin L 1995 Discreteness of area and volume in quantum gravity Nucl. Phys. B 442 593-619
14. Rovelli C and Smolin L 1995 Discreteness of area and volume in quantum gravity Nucl. Phys. B 456 734
15. Rovelli C 1996 Loop quantum gravity and black hole physics Helv. Phys. Acta 69 582
16. Perez A 2003 Spin foam models for quantum gravity Class. Quantum Grav. 20 R43
17. Rovelli C 1993 A generally covariant quantum field theory and a prediction on quantum measurements of geometry Nucl. Phys. B 405 797-816
18. Bojowald M and Kastrup H A 2000 Quantum symmetry reduction for diffeomorphism invariant theories of connections Class. Quantum Grav. 17 3009-43
19. Bojowald M and Kastrup H A 2001 Symmetric states in quantum geometry arXiv:gr-qc/0101061
20. Koslowski T 2006 Reduction of a quantum theory arXiv:gr-qc/0612138
21. Engle J 2006 Black hole entropy, constraints, and symmetry in quantum gravity PhD Thesis Penn State University (http://igpg.gravity.psu.edu/archives/ thesis/2006/englethesis.pdf)
22. Engle J 2007 Relating loop quantum cosmology to loop quantum gravity: symmetric sectors and embeddings arXiv:gr-qc/0701132
23. Brunnemann J and Fleischhack C 2007 On the configuration spaces of homogeneous loop quantum cosmology and loop quantum gravity arXiv:0709.1621v1
24. Martin-Benito M, Garay L J and Mena Marugan G A 2008 Hybrid quantum Gowdy cosmology: combining loop and Fock quantizations arXiv:0804.1098
25. Dittrich B and Tambornino J 2007 Gauge invariant perturbations around symmetry reduced sectors of general relativity: applications to cosmology Class. Quantum Grav. 24 4543 (arXiv:gr-qc/0702093)
26. Bojowald M 2006 Loop quantum cosmology and inhomogeneities Gen. Rel. Grav. 38 1771-95 (arXiv: gr-qc/0609034)
27. Bojowald M, Cartin D and Khanna G 2007 Lattice refining loop quantum cosmology, anisotropic models and stability Phys. Rev. D 76 064018 (arXiv:0704.1137)
28. Bojowald M, Hernandez H, Kagan M, Singh P and Skirzewski A 2007 Formation and evolution of structure in loop cosmology Phys. Rev. Lett. 98 031301 (arXiv:astro-ph/0611685)
29. Bojowald M and Swiderski R 2006 Spherically symmetric quantum geometry: Hamiltonian constraint Class. Quantum Grav. 23 2129-54 (arXiv:gr-qc/0511108)
30. Bojowald M, Hernandez H H and Morales-Tecotl H A 2006 Perturbative degrees of freedom in loop quantum gravity: anisotropies Class. Quantum Grav. 23 3491-516 (arXiv:gr-qc/0511058)
31. Bojowald M 2004 Spherically symmetric quantum geometry: states and basic operators Class. Quantum Grav. 21 3733-53 (arXiv:gr-qc/0407017)
32. Ellis G F R 2005 Relativistic cosmology http://www.pv.infn.it/ spacetimeinaction/speakers/transparencies>/Ellis/pdf/Ellis1.pdf, slide 58, Conference Spacetime in Action, Pavia
33. Thiemann T 2006 The Phoenix project: master constraint programme for loop quantum gravity Class. Quantum Grav. 23 2211-48
34. Engle J, Livine E, Pereira R and Rovelli C 2008 LQG vertex for general values of the Immirzi parameter Nucl. Phys. B 799 136-49 (arXiv:0711.0146)
35. Thiemann T 2001 Quantum spin dynamics (QSD) : VII. Symplectic structures and continuum lattice formulations of gauge field theories Class. Quantum Grav. 18 3293-338
36. Giesel K and Thiemann T 2006 Algebraic quantum gravity (AQG) I. Conceptual setup arXiv:gr-qc/0607099
37. Giesel K and Thiemann T 2007 Algebraic quantum gravity (AQG) IV. Reduced phase space quantisation of loop quantum gravity arXiv:0711.0119v1
38. Born M and Oppenheimer R 1927 Zur Quantentheorie der Molekeln Ann. Phys., Lpz. 17 457
39. Halliwell J and Hawking S 1985 Origin of structure in the universe Phys. Rev. D 31 1777-91
40. Vilenkin A 1989 Interpretation of the wavefunction of the universe Phys. Rev. D 39 1116-1122
41. Kiefer C 1994 The semiclassical approximation to QG in Canonical Quantum Gravity: From Classical To Quantum ed J Ehlers and H Friedrich (Berlin: Springer) pp 170-212
42. Kiefer C 2007 Quantum Gravity (Oxford: Oxford University Press)
43. Barrett J W, Galassi M, Miller W A, Sorkin R D, Tuckey P A and Williams R M 1994 A parallelizable implicit evolution scheme for Regge calculus arXiv:gr-qc/9411008v1
44. Modesto L and Rovelli C 2005 Particle scattering in loop quantum gravity Phys. Rev. Lett. 95 191301
45. Rovelli C 2006 Graviton propagator from background-independent quantum gravity Phys. Rev. Lett. 97 151301
46. Bianchi E, Modesto L, Rovelli C and Speziale S 2006 Graviton propagator in loop quantum gravity Class. Quantum Grav. 23 6989-7028
47. Livine E R and Speziale S 2006 Group integral techniques for the spinfoam graviton propagator J. High Energy Phys. JHEP11(2006)092
48. Speziale S 2006 Towards the graviton from spinfoams: the 3D toy model J. High Energy Phys. JHEP05(2006)039
49. Livine E R, Speziale S and Willis J L 2007 Towards the graviton from spinfoams: higher order corrections in the 3D toy model Phys. Rev. D 75 024038
50. Bianchi E and Modesto L 2007 The perturbative Regge-calculus regime of loop quantum gravity arXiv:0709.2051
51. Alesci E and Rovelli C 2007 The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex Phys. Rev. D 76 104012
52. Alesci E and Rovelli C 2008 The complete LQG propagator: II. Asymptotic behavior of the vertex Phys. Rev. D 77 044024
53. Einstein A 1917 Kosmologische Betrachtungen zur allgemeinen RelativitDtstheorie, Koniglich Preussische Akademie der Wissenschaften, Sitzungsberichte 1 421
54. Buchert T 2008 Dark energy from structure-a status report Gen. Rel. Grav. 40 467
55. Buchert T and Carfora M 2008 On the curvature of the present-day universe arXiv:0803.1401
56. Debbasch F 2004 What is a mean gravitational field? Eur. Phys. J. B 37 257-270
57. Rovelli C and Smolin L 1994 The physical Hamiltonian in nonperturbative quantum gravity Phys. Rev. Lett. 72 446
58. Ashtekar A 2006 Loop quantum cosmology of k = 1 FRW models arXiv:gr-qc/0612104
59. Engle J, Pereira R and Rovelli C 2007 The loop quantum gravity vertex amplitude Phys. Rev. Lett. 99 161301
60. Engle J, Pereira R and Rovelli C 2008 Flipped spinfoam vertex and loop gravity Nucl. Phys. B 798 251-90 (arXiv:0708.1236)
61. Livine E and Speziale S 2007 A new spinfoam vertex for quantum gravity Phys. Rev. D 76 084028 (arXiv:0705.0674)
62. Livine E and Speziale S 2008 Consistently solving the simplicity constraints for spinfoam quantum gravity Euro phys. Lett. 81 50004 (arXiv:0708.1915)
63. Freidel L and Krasnov K 2008 A new spin foam model for 4D gravity Class. Quantum Grav. 25 125018 (arXiv:0708.1595)
64. Alexandrov S 2007 Spin foam model from canonical quantization (arXiv:0705.3892)
65. Pereira R 2008 Lorentzian loop quantum gravity vertex amplitude Class. Quantum Grav. 25 085013
66. Barbieri A 1998 Quantum tetrahedra and simplicial spin networks Nucl. Phys. B 518 714-28
67. Baez J C and Barrett J W 1999 The quantum tetrahedron in 3 and 4 dimensions Adv. Theor. Math. Phys. 3 815-50
68. Ashtekar A, Corichi A and Zapata J A 1998 Quantum theory of geometry. III: Non-commutativity of Riemannian structures Class. Quantum Grav. 15 2955-72
69. Rovelli C and Speziale S 2006 A semiclassical tetrahedron Class. Quantum Grav. 23 5861-70