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Cosmological Applications of Loop Quantum Gravity

  • Part III Braneworlds, Loop Quantum Cosmology
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The Early Universe and Observational Cosmology

Part of the book series: Lecture Notes in Physics ((LNP,volume 646))

Abstract

After a brief introduction to classical and quantum gravity we discuss applications of loop quantum gravity in the cosmological realm. This includes the basic formalism and recent results of loop quantum cosmology, and a computation of modified dispersion relations for quantum gravity phenomenology. The presentation is held at a level which does not require much background knowledge in general relativity or mathematical techniques such as functional analysis, so as to make the article accessible to graduate students and researchers from other fields.

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References

  • 1. R. Arnowitt, S. Deser, and C. W. Misner: The Dynamics of General Relativity. In Gravitation: An Introduction to Current Research, ed by L. Witten (Wiley, New York 1962)

    Google Scholar 

  • 2. A. Ashtekar: Phys. Rev. D 36, 1587 (1987)

    Article  Google Scholar 

  • 3. J. F. Barbero G.: Phys. Rev. D 51, 5507 (1995), [gr-qc/9410014]

    Article  Google Scholar 

  • 4. A. Ashtekar, C. Beetle, O. Dreyer, S. Fairhurst, B. Krishnan, J. Lewandowski, and J. Wisniewski: Phys. Rev. Lett. 85 (2000) 3564, [gr-qc/0006006]; A. Ashtekar, C. Beetle, and J. Lewandowski: Class. Quantum Grav. 19, 1195 (2002), [gr-qc/0111067]

    Article  MATH  Google Scholar 

  • 5. A. Ashtekar, J. C. Baez, A. Corichi, and K. Krasnov: Phys. Rev. Lett. 80, 904 (1998), [gr-qc/9710007]; A. Ashtekar, J. C. Baez, and K. Krasnov: Adv. Theor. Math. Phys. 4, 1 (2001), [gr-qc/0005126]

    Article  MathSciNet  MATH  Google Scholar 

  • 6. A. Friedmann: Z. Phys. 10, 377 (1922)

    Google Scholar 

  • 7. F. Lucchin and S. Matarrese: Phys. Lett. B164, 282 (1985); Phys. Rev. D 32, 1316 (1985)

    Google Scholar 

  • 8. S. W. Hawking and G. F. R. Ellis: The Large Scale Structure of Space-Time (Cambridge University Press 1973)

    Google Scholar 

  • 9. D. L. Wiltshire: An introduction to quantum cosmology. In Cosmology: The Physics of the Universe, ed by B. Robson, N. Visvanathan, and W. S. Woolcock (World Scientific, Singapore 1996), pages 473–531, [gr-qc/0101003]

    Google Scholar 

  • 10. B. S. DeWitt: Phys. Rev. 160, 1113 (1967)

    Article  Google Scholar 

  • 11. P. G. Bergmann: Rev. Mod. Phys. 33, 510 (1961); C. Rovelli: Phys. Rev. D 43, 442 (1991)

    Article  Google Scholar 

  • 12. N. Kontoleon and D. L. Wiltshire: Phys. Rev. D 59, 063513 (1999), [gr-qc/9807075]

    Article  Google Scholar 

  • 13. A. Vilenkin: Phys. Rev. D 30, 509 (1984)

    Article  Google Scholar 

  • 14. J. B. Hartle and S. W. Hawking: Phys. Rev. D 28, 2960 (1983)

    Article  MathSciNet  Google Scholar 

  • 15. A. Ashtekar: Lectures on non-perturbative canonical gravity (World Scientific, Singapore 1991)

    Google Scholar 

  • 16. C. Rovelli: Liv. Rev. Relat. 1, 1 (1998), http://www.livingreviews.org/ Articles/Volume1/1998–1rovelli, [gr-qc/9710008].

    Google Scholar 

  • 17. T. Thiemann: Introduction to Modern Canonical Quantum General Relativity, [gr-qc/0110034]

    Google Scholar 

  • 18. M. Bojowald and H. A. Kastrup: Class. Quantum Grav. 17, 3009 (2000), [hep-th/9907042]

    Article  Google Scholar 

  • 19. R. Haag: Local quantum physics: Fields, particles, algebras (Springer, Berlin 1992)

    Google Scholar 

  • 20. H. Sahlmann: Some Comments on the Representation Theory of the Algebra Underlying Loop Quantum Gravity, [gr-qc/0207111]; When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?, [gr-qc/0207112]; H. Sahlmann and T. Thiemann: On the superselection theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories, [gr-qc/0302090; Irreducibility of the Ashtekar–Isham–Lewandowski representation, [gr-qc/0303074]; A. Okolow and J. Lewandowski: Class. Quantum Grav. 20, 3543 (2003), [gr-qc/0302059]

    Article  Google Scholar 

  • 21. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, and T. Thiemann: J. Math. Phys. 36, 6456 (1995), [gr-qc/9504018]

    Article  MathSciNet  MATH  Google Scholar 

  • 22. A. Ashtekar and J. Lewandowski: J. Geom. Phys. 17, 191 (1995), [hep-th/9412073]

    Article  MathSciNet  MATH  Google Scholar 

  • 23. A. Ashtekar and J. Lewandowski: J. Math. Phys. 36, 2170 (1995)

    MATH  Google Scholar 

  • 24. A. Ashtekar and J. Lewandowski: Background independent quantum gravity: A status report, in preparation

    Google Scholar 

  • 25. C. Rovelli and L. Smolin: Nucl. Phys. B331, 80 (1990)

    Google Scholar 

  • 26. C. Rovelli and L. Smolin: Phys. Rev. D 52, 5743 (1995)

    Article  Google Scholar 

  • 27. C. Rovelli and L. Smolin: Nucl. Phys. B442, 593 (1995), [gr-qc/9411005], Erratum: Nucl. Phys. B456, 753 (1995)

    Google Scholar 

  • 28. A. Ashtekar and J. Lewandowski: Class. Quantum Grav. 14, A55 (1997), [gr-qc/9602046]

    Google Scholar 

  • 29. A. Ashtekar and J. Lewandowski: Adv. Theor. Math. Phys. 1, 388 (1997), [gr-qc/9711031]

    Google Scholar 

  • 30. T. Thiemann: J. Math. Phys. 39, 3372 (1998), [gr-qc/9606092]

    Article  Google Scholar 

  • 31. T. Thiemann: J. Math. Phys. 39, 3347 (1998), [gr-qc/9606091]

    Article  Google Scholar 

  • 32. T. Thiemann: Phys. Lett. B 380, 257 (1996), [gr-qc/9606088]; Class. Quantum Grav. 15, 839 (1998), [gr-qc/9606089

    Article  Google Scholar 

  • 33. T. Thiemann: Class. Quantum Grav. 15, 1281 (1998), [gr-qc/9705019]

    Article  Google Scholar 

  • 34. M. Bojowald, Quantum Geometry and Symmetry (Shaker-Verlag, Aachen 2000)

    Google Scholar 

  • 35. M. Bojowald: Class. Quantum Grav. 17, 1489 (2000), [gr-qc/9910103]

    Article  Google Scholar 

  • 36. A. Ashtekar, M. Bojowald, and J. Lewandowski: Adv. Theor. Math. Phys., 7, 233 (2003), [gr-qc/0304074]

    Google Scholar 

  • 37. M. Bojowald: Class. Quantum Grav. 19, 2717 (2002), [gr-qc/0202077]

    Article  Google Scholar 

  • 38. M. Bojowald: Class. Quantum Grav. 17, 1509 (2000), [gr-qc/9910104]

    Article  Google Scholar 

  • 39. M. Bojowald: Class. Quantum Grav. 18, 1055 (2001), [gr-qc/0008052]

    Article  Google Scholar 

  • 40. M. Bojowald: Phys. Rev. D 64, 084018 (2001), [gr-qc/0105067]

    Article  Google Scholar 

  • 41. M. Bojowald: Class. Quantum Grav. 19, 5113 (2002), [gr-qc/0206053]

    Article  Google Scholar 

  • 42. M. Bojowald: Gen. Rel. Grav. 35, to appear (2003), [gr-qc/0305069]

    Google Scholar 

  • 43. M. Bojowald and K. Vandersloot: Phys. Rev. D 67, 124023 (2003), [gr-qc/0303072]

    Article  Google Scholar 

  • 44. M. Bojowald: Class. Quantum Grav. 18, L109 (2001), [gr-qc/0105113]

    Google Scholar 

  • 45. M. Bojowald: Phys. Rev. Lett. 86, 5227 (2001), [gr-qc/0102069]

    Article  Google Scholar 

  • 46. M. Bojowald: Phys. Rev. Lett. 87, 121301 (2001), [gr-qc/0104072]

    Article  Google Scholar 

  • 47. M. Bojowald and F. Hinterleitner: Phys. Rev. D 66, 104003 (2002), [gr-qc/0207038]

    Article  Google Scholar 

  • 48. M. Bojowald: Phys. Rev. Lett. 89, 261301 (2002), [gr-qc/0206054]

    Article  Google Scholar 

  • 49. M. Bojowald: Class. Quantum Grav. 20, 2595 (2003), [gr-qc/0303073]

    Article  Google Scholar 

  • 50. V. A. Belinskii, I. M. Khalatnikov, and E. M. Lifschitz: Adv. Phys. 13, 639 (1982)

    Google Scholar 

  • 51. D. Hobill, A. Burd, and A. Coley: Deterministic chaos in general relativity (Plenum Press, New York 1994)

    Google Scholar 

  • 52. M. Bojowald, G. Date, and K. Vandersloot: Homogeneous loop quantum cosmology: The role of the spin connection, [gr-qc/0311004]

    Google Scholar 

  • 53. P. Huet and M. Peskin: Nucl. Phys. B 434, 3 (1995); J. Ellis, J. López, N. E. Mavromatos and D. V. Nanopoulos: Phys. Rev. D 53, 3846 (1996)

    Article  Google Scholar 

  • 54. G. Amelino-Camelia, J. Ellis, N. E. Mavromatos, D. V. Nanopoulos and S. Sarkar: Nature 393, 763 (1998)

    Article  Google Scholar 

  • 55. R. J. Gleiser and C. N. Kozameh: Phys. Rev. D 64, 083007 (2001), [gr-qc/0102093]

    Article  Google Scholar 

  • 56. G. Amelino-Camelia: Nature 398, 216 (1999), [gr-qc/9808029]

    Article  Google Scholar 

  • 57. Y. J. Ng and H. van Dam: Found. Phys. 30, 795 (2000), [gr-qc/9906003]

    Article  Google Scholar 

  • 58. R. Brustein, D. Eichler and S. Foffa: Phys. Rev. D 65, 105006 (2002)

    Article  Google Scholar 

  • 59. T. Kifune: Astrophys. J. Lett. 518, L21 (1999), [astro-ph/9904164]

    Google Scholar 

  • 60. G. Amelino-Camelia and T. Piran: Phys. Rev. D 64, 036005 (2001), [gr-qc/0008107]

    Article  Google Scholar 

  • 61. J. Alfaro and G. Palma: Phys. Rev. D 65, 103516 (2002), [hep-th/0111176; Phys. Rev. D 67, 083003 (2003), [hep-th/0208193]

    Article  Google Scholar 

  • 62. T. J. Konopka and S. A. Major: New Journal of Physics 4, 57 (2002), [hep-ph/0201184]

    Article  Google Scholar 

  • 63. J. R. Ellis, J. L. López, N. E. Mavromatos and D. V. Nanopoulos: Phys. Rev. D 53, 3846 (1996), [hep-ph/9505340]

    Article  Google Scholar 

  • 64. D. Sudarsky, L. F. Urrutia and H. Vucetich: Phys. Rev. Lett. 89, 231301 (2002), [gr-qc/0204027]

    Article  Google Scholar 

  • 65. J. Ellis, N. E. Mavromatos and D. V. Nanopoulos: Gen. Rel. Grav. 31, 1257 (1999), [gr-qc/9905048]; G. Z. Adunas, E. Rodriguez-Milla and D. V. Ahluwalia: Phys. Lett. B 485, 215 (2000), [gr-qc/0006021]; G. Amelino-Camelia: Lect. Notes Phys. 541, 1–49 (2000), [gr-qc/9910089]

    Article  MathSciNet  MATH  Google Scholar 

  • 66. J. van Paradis et al.: Nature 386, 686 (1997); M. L. Metzger et al.: Nature 387, 878 (1997)

    Article  Google Scholar 

  • 67. P. N. Bhat, G. J. Fishman, C. A. Meegan, R. B. Wilson, M. N. Brock and W. S. Paclesas: Nature 359, 217 (1992)

    Article  Google Scholar 

  • 68. P. Mészáros: Nucl. Phys. B (Proc. Suppl.) 80, 63 (2000)

    Article  Google Scholar 

  • 69. S. D. Biller et al.: Phys. Rev. Lett. 83, 2108 (1999)

    Article  Google Scholar 

  • 70. E. Waxman and J. Bahcall: Phys. Rev. Lett. 78, 2292 (1997); E. Waxman: Nucl. Phys. B (Proc. Suppl.) 91, 494 (2000); Nucl. Phys. B (Proc. Suppl.) 87, 345 (2000)

    Article  Google Scholar 

  • 71. M. Vietri: Phys. Rev. Lett. 80, 3690 (1998)

    Article  Google Scholar 

  • 72. M. Roy, H. J. Crawford and A. Trattner: The prediction and detection of UHE Neutrino Bursts, [astro-ph/9903231]

    Google Scholar 

  • 73. S. Choubey and S. F. King: Phys. Rev. D 67, 073005 (2003), [hep-ph/0207260]

    Article  Google Scholar 

  • 74. R. Gambini and J. Pullin: Phys. Rev. D 59, 124021 (1999), [gr-qc/9809038]

    Article  Google Scholar 

  • 75. J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia: Phys. Rev. D 65, 103509 (2002), [hep-th/0108061]

    Article  Google Scholar 

  • 76. J. Alfaro, H. A. Morales-Técotl, and L. F. Urrutia: Phys. Rev. Lett. 84, 2318 (2000), [gr-qc/9909079]; Phys. Rev. D 66, 124006 (2002), [hep-th/0208192].

    Article  Google Scholar 

  • 77. N. E. Mavromatos, The quest for quantum gravity: testing times for theories?, [astro-ph/0004225]; J. Ellis, Perspectives in High-Energy Physics, JHEP Proceedings (2000), [hep-ph/0007161]; J. Ellis, Testing fundamental physics with high-energy cosmic rays, Nuovo Cim. C 24, 483 (2001), [astro-ph/0010474]

    Google Scholar 

  • 78. F. Benatti and R. Floreanini: Phys. Rev. D 64, 085015 (2001), [hep-ph/0105303]; Phys. Rev. D 62, 125009 (2000), [hep-ph/0009283]

    Article  Google Scholar 

  • 79. D. A. R. Dalvit, F. D. Mazzitelli, C. Molina-Paris: Phys. Rev. D 63, 084023 (2001), [hep-th/0010229].

    Article  Google Scholar 

  • 80. T. Padmanabhan: Phys. Rev. D 57, 6206 (1998); K. Srinivasan, L. Sriramkumar and T. Padmanabhan: Phys. Rev. D 58, 044009 (1998); S. Shankaranarayanan and T. Padmanabhan: Int. J. Mod. Phys. D 10, 351 (2001)

    Article  Google Scholar 

  • 81. G. Amelino-Camelia, T. Piran: Phys. Lett. B497, 265 (2001), [[hep-ph /0006210]

    Google Scholar 

  • 82. For recent reviews see V. A. Kostelecky: Topics in Lorentz and CPT violation, [hep-ph/0104227; R. Bluhm: Probing the Planck scale in low-energy atomic physics, [hep-ph/0111323], and references therein.

    Google Scholar 

  • 83. J. M. Carmona and J. L. Cortés: Phys. Lett. B494, 75 (2000), [hep-ph/0007057]

    Google Scholar 

  • 84. S. Liberati, T. Jacobson and D. Mattingly: High-energy constraints on Lorentz symmetry violations, hep-ph/0110094; T. Jacobson, S. Liberati and D. Mattingly, Phys. Rev. D 66, 081302 (2002), [hep-ph/0112207].

    Google Scholar 

  • 85. R. C. Myers, M. Pospelov: Phys. Rev. Lett.90, 211601 (2003), [hep-ph/0301124].

    Google Scholar 

  • 86. A. Ashtekar, C. Rovelli and L. Smolin: Phys. Rev. Lett. 69, 237 (1992), [hep-th/9203079]

    Article  MathSciNet  MATH  Google Scholar 

  • 87. T. Thiemann: Class. Quantum Grav. 18, 2025 (2001), [hep-th/0005233]

    Article  Google Scholar 

  • 88. H. Sahlmann, T. Thiemann, and O. Winkler: Nucl. Phys. B 606, 401 (2001), [gr-qc/0102038]

    Article  MathSciNet  MATH  Google Scholar 

  • 89. M. Varadarajan: Phys. Rev. D 64, 104003 (2001), [gr-qc/0104051]

    Article  Google Scholar 

  • 90. A. Ashtekar and J. Lewandowski: Class. Quantum Grav. 18, L117 (2001), [gr-qc/0107043]

    Google Scholar 

  • 91. For the analogous situation in electrodynamics see for example W. Heitler: Quantum Theory of Radiation, 3rd edn (Clarendon Press, Oxford, England 1954)

    Google Scholar 

  • 92. H. Sahlmann and T. Thiemann: Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme, gr-qc/0207030; II: A Concrete Implementation, [gr-qc/0207031]

    Google Scholar 

  • 93. G. Amelino-Camelia: Int. J. Mod. Phys. D 12, 1633 (2003), [gr-qc/0305057]

    Article  Google Scholar 

  • 94. G. Amelino-Camelia: Int. J. Mod. Phys. D 11, 35 (2002); J. Magueijo and L. Smolin: Phys. Rev. Lett. 88, 190403 (2002), [hep-th/0112090]

    Article  MathSciNet  Google Scholar 

  • 95. T. Jacobson and D. Mattingly: Phys. Rev. D 63, 041502(R) (2001)

    Article  Google Scholar 

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Authors and Affiliations

  1. Center for Gravitational Physics and Geometry, The Pennsylvania State University, University Park, PA 16802, USA.

    Martin Bojowald

  2. Departamento de Física, Universidad Autónoma Metropolitana Iztapalapa, A.P. 55-534 México D.F. 09340, México

    Hugo A. Morales-Técotl

  3. Associate member of AS-ICTP Trieste, Italy

    Hugo A. Morales-Técotl

Authors
  1. Martin Bojowald
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  2. Hugo A. Morales-Técotl
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Nora Bretón Jorge Luis Cervantes-Cota Marcelo Salgado

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Bojowald, M., Morales-Técotl, H.A. Cosmological Applications of Loop Quantum Gravity. In: Bretón, N., Cervantes-Cota, J.L., Salgado, M. (eds) The Early Universe and Observational Cosmology. Lecture Notes in Physics, vol 646. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40918-2_17

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