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Cited by 723Noncommutative and Quantum Gravity TheoriesCosmology and Gravitation TheoriesRelativity and Gravitational Theory

Loop Quantum Cosmology

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Bojowald, Martin·2005·Living Reviews in Relativity
DOI 10.12942/lrr-2005-11PMC PMC5253914
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Abstract

Quantum gravity is expected to be necessary in order to understand situations where classical general relativity breaks down. In particular in cosmology one has to deal with initial singularities, i.e., the fact that the backward evolution of a classical space-time inevitably comes to an end after a finite amount of proper time. This presents a breakdown of the classical picture and requires an extended theory for a meaningful description. Since small length scales and high curvatures are involved, quantum effects must play a role. Not only the singularity itself but also the surrounding space-time is then modified. One particular realization is loop quantum cosmology, an application of loop quantum gravity to homogeneous systems, which removes classical singularities. Its implications can be studied at different levels. Main effects are introduced into effective classical equations which allow to avoid interpretational problems of quantum theory. They give rise to new kinds of early universe phenomenology with applications to inflation and cyclic models. To resolve classical singularities and to understand the structure of geometry around them, the quantum description is necessary. Classical evolution is then replaced by a difference equation for a wave function which allows to extend space-time beyond classical singularities. One main question is how these homogeneous scenarios are related to full loop quantum gravity, which can be dealt with at the level of distributional symmetric states. Finally, the new structure of space-time arising in loop quantum gravity and its application to cosmology sheds new light on more general issues such as time. ELECTRONIC SUPPLEMENTARY MATERIAL: Supplementary material is available for this article at 10.12942/lrr-2005-11.

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Research works printed but not linked: 38

  1. [1]Alexander, S., “A Quantum Gravitational Relaxation of The Cosmological Constant”, (2005). URL (cited on 09 October 2005): http://arXiv.org/abs/hep-th/0503146. · arXiv
  2. [4]Alfaro J Morales-Técotl HA Urrutia LF Loop quantum gravity and light propagation Phys. Rev. D 2002 65 103509 10.1103/PhysRevD.65.103509 11018874 · DOI
  3. [6]Arnowitt R Deser S Misner CW Witten L The dynamics of general relativity Gravitation: An Introduction to Current Research 1962 New York, U.S.A. Wiley 227 265
  4. [9]Ashtekar A Bishop NT Maharaj SD Quantum Geometry and Gravity: Recent Advances General Relativity and Gravitation 2002 Singapore; River Edge, U.S.A. World Scientific
  5. [14]Ashtekar, A., and Bojowald, M., “Quantum Geometry and the Schwarzschild Singularity”, (2005). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0509075. · arXiv
  6. [26]Ashtekar A Schilling TA Harvey A Geometrical Formulation of Quantum Mechanics On Einstein’s Path: Essays in Honor of Engelbert Schücking 1999 New York, U.S.A. Springer 23 65
  7. [53]Bojowald M Cosmology: Original questions Nature 2005 436 920 921 10.1038/436920a 16107822 · DOI
  8. [54]Bojowald, M., “Degenerate Configurations, Singularities and the Non-Abelian Nature of Loop Quantum Gravity”, (2005). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0508118. · arXiv
  9. [56]Bojowald M Ashtekar A Loop Quantum Cosmology 100 Years of Relativity. Space-Time Structure: Einstein and Beyond 2005 Singapore World Scientific
  10. [63]Bojowald, M., Hernandez, H.H., and Morales-Técotl, H.A., “Perturbative degrees of freedom in loop quantum gravity: Anisotropies”, (2005). URL (cited on 06 December 2005): http://arXiv.org/abs/gr-qc/0511058. · arXiv
  11. [65]Bojowald M Kastrup HA Gurzadyan VG Jantzen RT Ruffini R Symmetric States in Quantum Geometry The Ninth Marcel Grossmann Meeting: On recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories, Part B 2000 Singapore; River Edge, U.S.A. World Scientific 1271 1272
  12. [69]Bojowald M Morales-Técotl HA Bretón N Cervantes-Cota JL Salgado M Cosmological applications of loop quantum gravity The Early Universe and Observational Cosmology 2004 Berlin, Germany; New York, U.S.A. Springer 421 462
  13. [75]Bojowald, M., and Swiderski, R., “Spherically Symmetric Quantum Geometry: Hamiltonian Constraint”, (2005). URL (cited on 06 December 2005): http://arXiv.org/abs/gr-qc/0511108. · arXiv
  14. [78]Bojowald M Vandersloot K Novello M Perez-Bergliaffa S Ruffini R Loop Quantum Cosmology and Boundary Proposals The Tenth Marcel Grossmann Meeting: On recent developments in theoretical and experimental general relativity, gravitation, and relativistic field theories 2005 Singapore World Scientific
  15. [81]Brocker T Tom Dieck T Representations of Compact Lie Groups 1995 2 New York, U.S.A. Springer
  16. [83]Brunnemann, J., and Thiemann, T., “Simplification of the Spectral Analysis of the Volume Operator in Loop Quantum Gravity”, (2004). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0405060. · arXiv
  17. [84]Brunnemann, J., and Thiemann, T., “On (Cosmological) Singularity Avoidance in Loop Quantum Gravity”, (2005). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0505032. · arXiv
  18. [85]Brunnemann, J., and Thiemann, T., “Unboundedness of Triad-Like Operators in Loop Quantum Gravity”, (2005). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0505033. · arXiv
  19. [88]Connors, S., and Khanna, G., “Approximate pre-classical solutions in loop quantum cosmology”, (2005). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0509081. · arXiv
  20. [105]Dirac PAM Lectures on Quantum Mechanics 1964 New York, U.S.A. Yeshiva Press
  21. [106]Dittrich, B., “Partial and Complete Observables for Hamiltonian Constrained Systems”, (2004). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0411013. · arXiv
  22. [107]Dittrich, B., and Loll, R., “Counting a black hole in Lorentzian product triangulations”, (2004). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0506035. · arXiv
  23. [122]Hawking SW Ellis GFR The Large Scale Structure of Space-Time 1973 Cambridge, U.K. Cambridge University Press
  24. [132]Husain, V., and Winkler, O., “Quantum black holes”, (2004). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0412039. · arXiv
  25. [135]Kasner E Geometrical Theorems on Einstein’s Cosmological Equations Am. J. Math. 1921 43 217 10.2307/2370192 17818870 · DOI
  26. [138]Kobayashi S Nomizu K Foundations of Differential Geometry 1963 New York, U.S.A. John Wiley
  27. [139]Kobayashi S Nomizu K Foundations of Differential Geometry 1969 New York, U.S.A. John Wiley
  28. [143]Kuchar KV Kunstatter G Vincent DE Williams JG Time and interpretations of quantum gravity General Relativity and Relativistic Astrophysics 1992 Singapore; River Edge, U.S.A. World Scientific
  29. [146]Lewandowski, J., Okolów, A., Sahlmann, H., and Thiemann, T., “Uniqueness of diffeomorphism invariant states on holonomy-flux algebras”, (2005). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0504147. · arXiv
  30. [163]Nunes, N.J., “Inflation: A graceful entrance from Loop Quantum Cosmology”, (2005). URL (cited on 09 October 2005): http://arXiv.org/abs/astro-ph/0507683. · arXiv
  31. [168]Rendall AD Ashtekar A The Nature of Spacetime Singularities 100 Years of Relativity. Space-Time Structure: Einstein and Beyond 2005 Singapore World Scientific
  32. [174]Rovelli C Quantum Gravity 2004 Cambridge, U.K.; New York, U.S.A. Cambridge University Press
  33. [179]Sahlmann, H., “Some Comments on the Representation Theory of the Algebra Underlying Loop Quantum Gravity”, (2002). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0207111. · arXiv
  34. [180]Sahlmann, H., “When Do Measures on the Space of Connections Support the Triad Operators of Loop Quantum Gravity?”, (2002). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0207112. · arXiv
  35. [181]Sahlmann, H., and Thiemann, T., “Towards the QFT on Curved Spacetime Limit of QGR. I: A General Scheme”, (2002). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0207030. · arXiv
  36. [182]Sahlmann, H., and Thiemann, T., “Towards the QFT on Curved Spacetime Limit of QGR. II: A Concrete Implementation”, (2002). URL (cited on 09 October 2005): http://arXiv.org/abs/gr-qc/0207031. · arXiv
  37. [190]Smolin, L., “An invitation to loop quantum gravity”, (2004). URL (cited on 09 October 2005): http://arXiv.org/abs/hep-th/0408048. · arXiv
  38. [193]Thiemann T QSD V: Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories Class. Quantum Grav. 1998 15 1281 1314 10.1088/0264-9381/15/5/012 · DOI · Paper page

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Authors
Bojowald, M.
Affiliations
Pennsylvania State University (US)
Corresponding author
Bojowald, Martin
Venue
Living Reviews in Relativity
Publisher
Springer Science and Business Media LLC
Published
2005-12
Volume
8
Issue
1
Pages
11-11
ISSN
  • 1433-8351 (ISSN-L)
  • 2367-3613
DOI
10.12942/lrr-2005-11
PMC
PMC5253914
OpenAlex
W2109902906
Cited by
723
References
156
Citations by year
2026: 19 · 2025: 25 · 2024: 26 · 2023: 19 · 2022: 27 · 2021: 32 · 2020: 27 · 2019: 29 · 2018: 22 · 2017: 26 · 2016: 26 · 2015: 30 · 2014: 25 · 2013: 45 · 2012: 45
FWCI
3.89
Type
journal article
Language
en
Update notices
new_version (2008-07-02)
Open access
Licence
cc-by
Locations
  • Living Reviews in Relativity (publishedVersion, cc-by)
  • PubMed Central (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
Keywords
loop quantum cosmology, loop quantum gravity, initial singularity, singularity resolution, early universe, inflation (cosmology), cyclic cosmology, recurrence relations, wave function of the universe, nature of time, quantum gravity

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