Skip to main content
SpringerLink
Log in

Loop Quantum Cosmology, Space-Time Structure, and Falsifiability

  • Chapter
Quantum Gravity and Quantum Cosmology

Part of the book series: Lecture Notes in Physics ((LNP,volume 863))

  • 3540 Accesses

Abstract

Loop quantum cosmology attempts to understand the full dynamics of loop quantum gravity by realizing crucial effects in simpler, usually symmetric settings. Several subtleties arise especially when cosmological questions are to be addressed, related to possible mini-superspace artefacts, consistent cosmological perturbation theory, and quantum space-time structure. Recent work on inhomogeneous perturbations has highlighted some of the dangers of an over-reliance on simple models, sometimes not just reduced by symmetry but also in the possible forms of matter or quantum corrections. Only a consistent treatment of inhomogeneity, taking into account the full gauge structure related to general covariance, can show what happens at high densities in quantum gravity. The relevant methods and results (especially effective equations, potential observational signatures, singularity resolution and signature change) are surveyed in here.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 79.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. M. Bojowald, Class. Quantum Gravity 17, 1489 (2000). gr-qc/9910103

    Article  ADS  MathSciNet  Google Scholar 

  2. M. Bojowald, Living Rev. Relativ. 11, 4 (2008). http://www.livingreviews.org/lrr-2008-4. gr-qc/0601085

    Article  ADS  Google Scholar 

  3. M. Bojowald, Quantum Cosmology: A Fundamental Theory of the Universe (Springer, New York, 2011)

    Book  MATH  Google Scholar 

  4. C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, 2004)

    Book  MATH  Google Scholar 

  5. T. Thiemann, Introduction to Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, 2007)

    Book  MATH  Google Scholar 

  6. A. Ashtekar, J. Lewandowski, Class. Quantum Gravity 21, R53 (2004). gr-qc/0404018

    Article  ADS  MathSciNet  Google Scholar 

  7. K.V. Kuchař, M.P. Ryan, Phys. Rev. D 40, 3982 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  8. M. Bojowald, H.A. Kastrup, Class. Quantum Gravity 17, 3009 (2000). hep-th/9907042

    Article  ADS  MathSciNet  Google Scholar 

  9. M. Bojowald, Class. Quantum Gravity 19, 2717 (2002). gr-qc/0202077

    Article  ADS  MathSciNet  Google Scholar 

  10. A. Ashtekar, M. Bojowald, J. Lewandowski, Adv. Theor. Math. Phys. 7, 233 (2003). gr-qc/0304074

    Article  MathSciNet  Google Scholar 

  11. B.S. DeWitt, Phys. Rev. 160, 1113 (1967)

    Article  ADS  Google Scholar 

  12. D.L. Wiltshire, in Cosmology: The Physics of the Universe, ed. by B. Robson, N. Visvanathan, W.S. Woolcock (World Scientific, Singapore, 1996), pp. 473–531. gr-qc/0101003

    Google Scholar 

  13. M. Bojowald, Class. Quantum Gravity 17, 1509 (2000). gr-qc/9910104

    Article  ADS  MathSciNet  Google Scholar 

  14. M. Bojowald, Class. Quantum Gravity 18, 1055 (2001). gr-qc/0008052

    Article  ADS  MathSciNet  Google Scholar 

  15. M. Bojowald, Class. Quantum Gravity 18, 1071 (2001). gr-qc/0008053

    Article  ADS  MathSciNet  Google Scholar 

  16. A. Ashtekar, T. Pawłowski, P. Singh, Phys. Rev. D 73, 124038 (2006). gr-qc/0604013

    Article  ADS  MathSciNet  Google Scholar 

  17. A. Ashtekar, T. Pawłowski, P. Singh, Phys. Rev. D 74, 084003 (2006). gr-qc/0607039

    Article  ADS  MathSciNet  Google Scholar 

  18. W.F. Blyth, C.J. Isham, Phys. Rev. D 11, 768 (1975)

    Article  ADS  MathSciNet  Google Scholar 

  19. W. Kaminski, J. Lewandowski, Class. Quantum Gravity 25, 035001 (2008). arXiv:0709.3120

    Article  MathSciNet  Google Scholar 

  20. W. Kaminski, T. Pawłowski, Phys. Rev. D 81, 024014 (2010). arXiv:0912.0162

    Article  ADS  Google Scholar 

  21. M. Martín-Benito, L.J. Garay, G.A. Mena Marugán, Phys. Rev. D 78, 083516 (2008). arXiv:0804.1098

    Article  ADS  MathSciNet  Google Scholar 

  22. D. Brizuela, G.A. Mena Marugán, T. Pawłowski, Class. Quantum Gravity 27, 052001 (2010). arXiv:0902.0697

    Article  ADS  Google Scholar 

  23. A. Ashtekar, M. Campiglia, A. Henderson, Phys. Lett. B 681, 347 (2009). arXiv:0909.4221

    Article  ADS  MathSciNet  Google Scholar 

  24. A. Ashtekar, M. Campiglia, A. Henderson, Class. Quantum Gravity 27, 135020 (2010). arXiv:1001.5147

    Article  ADS  MathSciNet  Google Scholar 

  25. C. Rovelli, F. Vidotto, Class. Quantum Gravity 27, 145005 (2010). arXiv:0911.3097

    Article  ADS  MathSciNet  Google Scholar 

  26. A. Henderson, C. Rovelli, F. Vidotto, E. Wilson-Ewing, Class. Quantum Gravity 28, 025003 (2011). arXiv:1010.0502

    Article  ADS  MathSciNet  Google Scholar 

  27. E. Bentivegna, T. Pawłowski, Phys. Rev. D 77, 124025 (2008). arXiv:0803.4446

    Article  ADS  MathSciNet  Google Scholar 

  28. M. Martín-Benito, G.A. Mena Marugán, T. Pawłowski, Phys. Rev. D 80, 084038 (2009). arXiv:0906.3751

    Article  ADS  MathSciNet  Google Scholar 

  29. G.A. Mena Marugán, J. Olmedo, T. Pawłowski, Phys. Rev. D 84, 064012 (2011). arXiv:1108.0829

    Article  ADS  Google Scholar 

  30. M. Bojowald, Phys. Rev. D 75, 081301(R) (2007). gr-qc/0608100

    Article  ADS  MathSciNet  Google Scholar 

  31. M. Bojowald, Phys. Rev. D 75, 123512 (2007). gr-qc/0703144

    Article  ADS  MathSciNet  Google Scholar 

  32. K. Vandersloot, Phys. Rev. D 71, 103506 (2005). gr-qc/0502082

    Article  ADS  MathSciNet  Google Scholar 

  33. P. Singh, Phys. Rev. D 73, 063508 (2006). gr-qc/0603043

    Article  ADS  MathSciNet  Google Scholar 

  34. M. Bojowald, Phys. Rev. Lett. 100, 221301 (2008). arXiv:0805.1192

    Article  ADS  MathSciNet  Google Scholar 

  35. M. Bojowald, Gen. Relativ. Gravit. 40, 2659 (2008). arXiv:0801.4001

    Article  ADS  MathSciNet  Google Scholar 

  36. M. Bojowald, Phys. Rev. Lett. 86, 5227 (2001). gr-qc/0102069

    Article  ADS  MathSciNet  Google Scholar 

  37. M. Novello, S.E.P. Bergliaffa, Phys. Rep. 463, 127 (2008). arXiv:0802.1634

    Article  ADS  MathSciNet  Google Scholar 

  38. T. Cailleteau, J. Mielczarek, A. Barrau, J. Grain, arXiv:1111.3535

  39. M. Bojowald, G.M. Paily, arXiv:1112.1899

  40. M. Bojowald, in Foundations of Space and Time: Reflections on Quantum Gravity, ed. by J. Murugan, A. Weltman, G.F.R. Ellis (Cambridge University Press, Cambridge, 2012). arXiv:1101.5592

    Google Scholar 

  41. K. Banerjee, G. Calcagni, M. Martín-Benito, SIGMA 8, 016 (2012). arXiv:1109.6801

    Google Scholar 

  42. A. Perez, Class. Quantum Gravity 20, R43 (2003). gr-qc/0301113

    Article  ADS  Google Scholar 

  43. D. Oriti, Approaches to Quantum Gravity (Cambridge University Press, Cambridge, 2009)

    Book  MATH  Google Scholar 

  44. M. Bojowald, P.A. Höhn, A. Tsobanjan, Class. Quantum Gravity 28, 035006 (2011). arXiv:1009.5953

    Article  ADS  Google Scholar 

  45. M. Bojowald, P.A. Höhn, A. Tsobanjan, Phys. Rev. D 83, 125023 (2011). arXiv:1011.3040

    Article  ADS  Google Scholar 

  46. P.A. Höhn, E. Kubalova, A. Tsobanjan, arXiv:1111.5193

  47. P.A.M. Dirac, Proc. R. Soc. A 246, 333 (1958)

    Article  ADS  MathSciNet  Google Scholar 

  48. K.V. Kuchař, J. Math. Phys. 15, 708 (1974)

    Article  ADS  Google Scholar 

  49. S.A. Hojman, K. Kuchař, C. Teitelboim, Ann. Phys. 96, 88 (1976)

    Article  ADS  Google Scholar 

  50. J.F. Donoghue, Phys. Rev. D 50, 3874 (1994). gr-qc/9405057

    Article  ADS  Google Scholar 

  51. C.P. Burgess, Living Rev. Relativ. 7, 5 (2004). http://www.livingreviews.org/lrr-2004-5. gr-qc/0311082

    Article  ADS  Google Scholar 

  52. N. Kaloper, M. Kleban, A. Lawrence, S. Shenker, Phys. Rev. D 66, 123510 (2002). hep-th/0201158

    Article  ADS  Google Scholar 

  53. M. Bojowald, G. Hossain, M. Kagan, S. Shankaranarayanan, Phys. Rev. D 78, 063547 (2008). arXiv:0806.3929

    Article  ADS  MathSciNet  Google Scholar 

  54. G. Immirzi, Class. Quantum Gravity 14, L177 (1997). gr-qc/9612030

    Article  ADS  MathSciNet  Google Scholar 

  55. J.F. Barbero, Phys. Rev. D 51, 5507 (1995). gr-qc/9410014

    Article  ADS  MathSciNet  Google Scholar 

  56. A. Ashtekar, Phys. Rev. D 36, 1587 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  57. C. Rovelli, L. Smolin, Nucl. Phys. B 331, 80 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  58. C. Rovelli, L. Smolin, Nucl. Phys. B 442, 593 (1995). Erratum: Nucl. Phys. B 456, 753 (1995). gr-qc/9411005

    Article  ADS  MathSciNet  Google Scholar 

  59. A. Ashtekar, J. Lewandowski, Class. Quantum Gravity 14, A55 (1997). gr-qc/9602046

    Article  ADS  MathSciNet  Google Scholar 

  60. A. Perez, Phys. Rev. D 73, 044007 (2006). gr-qc/0509118

    Article  ADS  MathSciNet  Google Scholar 

  61. A. Henderson, A. Laddha, C. Tomlin, arXiv:1204.0211 [gr-qc]

  62. M. Bojowald, Gen. Relativ. Gravit. 38, 1771 (2006). gr-qc/0609034

    Article  ADS  MathSciNet  Google Scholar 

  63. M. Bojowald, Gen. Relativ. Gravit. 40, 639 (2008). arXiv:0705.4398

    Article  ADS  MathSciNet  Google Scholar 

  64. M. Bojowald, A. Skirzewski, Rev. Math. Phys. 18, 713 (2006). math-ph/0511043

    Article  MathSciNet  Google Scholar 

  65. M. Bojowald, A. Skirzewski, Int. J. Geom. Methods Mod. Phys. 4, 25 (2007). hep-th/0606232

    Article  MathSciNet  Google Scholar 

  66. T. Thiemann, Class. Quantum Gravity 15, 1281 (1998). gr-qc/9705019

    Article  ADS  MathSciNet  Google Scholar 

  67. M. Bojowald, Class. Quantum Gravity 26, 075020 (2009). arXiv:0811.4129

    Article  ADS  MathSciNet  Google Scholar 

  68. M. Bojowald, G. Calcagni, S. Tsujikawa, Phys. Rev. Lett. 107, 211302 (2011). arXiv:1101.5391

    Article  ADS  Google Scholar 

  69. M. Bojowald, G. Hossain, M. Kagan, S. Shankaranarayanan, Phys. Rev. D 79, 043505 (2009). arXiv:0811.1572

    Article  ADS  MathSciNet  Google Scholar 

  70. M. Bojowald, G. Calcagni, J. Cosmol. Astropart. Phys. 1103, 032 (2011). arXiv:1011.2779

    Article  ADS  Google Scholar 

  71. M. Bojowald, G. Hossain, Phys. Rev. D 77, 023508 (2008). arXiv:0709.2365

    Article  ADS  MathSciNet  Google Scholar 

  72. G. Calcagni, G. Hossain, Adv. Sci. Lett. 2, 184 (2009). arXiv:0810.4330

    Article  Google Scholar 

  73. M. Bojowald, G. Calcagni, S. Tsujikawa, J. Cosmol. Astropart. Phys. 1111, 046 (2011). arXiv:1107.1540

    Article  ADS  Google Scholar 

  74. E.J. Copeland, D.J. Mulryne, N.J. Nunes, M. Shaeri, Phys. Rev. D 77, 023510 (2008). arXiv:0708.1261

    Article  ADS  MathSciNet  Google Scholar 

  75. E.J. Copeland, D.J. Mulryne, N.J. Nunes, M. Shaeri, Phys. Rev. D 79, 023508 (2009). arXiv:0810.0104

    Article  ADS  Google Scholar 

  76. G. Calcagni, M.V. Cortês, Class. Quantum Gravity 24, 829 (2007). gr-qc/0607059

    Article  ADS  Google Scholar 

  77. M. Shimano, T. Harada, Phys. Rev. D 80, 063538 (2009). arXiv:0909.0334

    Article  ADS  Google Scholar 

  78. A. Barrau, J. Grain, Phys. Rev. Lett. 102, 081301 (2009). arXiv:0902.0145

    Article  ADS  MathSciNet  Google Scholar 

  79. J. Grain, A. Barrau, A. Gorecki, Phys. Rev. D 79, 084015 (2009). arXiv:0902.3605

    Article  ADS  Google Scholar 

  80. J. Grain, T. Cailleteau, A. Barrau, A. Gorecki, Phys. Rev. D 81, 024040 (2010). arXiv:0910.2892

    Article  ADS  Google Scholar 

  81. J. Mielczarek, T. Cailleteau, J. Grain, A. Barrau, Phys. Rev. D 81, 104049 (2010). arXiv:1003.4660

    Article  ADS  Google Scholar 

  82. J. Mielczarek, M. Szydłowski, Phys. Lett. B 657, 20 (2007). arXiv:0705.4449

    Article  ADS  Google Scholar 

  83. M. Bojowald, J.D. Reyes, R. Tibrewala, Phys. Rev. D 80, 084002 (2009). arXiv:0906.4767

    Article  ADS  MathSciNet  Google Scholar 

  84. J.D. Reyes, Ph.D. thesis, The Pennsylvania State University, 2009

    Google Scholar 

  85. A. Perez, D. Pranzetti, Class. Quantum Gravity 27, 145009 (2010). arXiv:1001.3292

    Article  ADS  MathSciNet  Google Scholar 

  86. T. Cailleteau, A. Barrau, arXiv:1111.7192

  87. F. Cametti, G. Jona-Lasinio, C. Presilla, F. Toninelli, in Proceedings of the International School of Physics ‘Enrico Fermi’, Course CXLIII (IOS Press, Amsterdam, 2000), pp. 431–448. quant-ph/9910065

    Google Scholar 

  88. M. Bojowald, A. Tsobanjan, Phys. Rev. D 80, 125008 (2009). arXiv:0906.1772

    Article  ADS  Google Scholar 

  89. M. Bojowald, D. Brizuela, H.H. Hernandez, M.J. Koop, H.A. Morales-Técotl, Phys. Rev. D 84, 043514 (2011). arXiv:1011.3022

    Article  ADS  Google Scholar 

  90. M. Bojowald, T. Strobl, Rev. Math. Phys. 15, 663 (2003). hep-th/0112074

    Article  MathSciNet  Google Scholar 

  91. M. Bojowald, Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity (Cambridge University Press, Cambridge, 2010)

    Book  MATH  Google Scholar 

  92. M. Bojowald, H. Hernández, A. Skirzewski, Phys. Rev. D 76, 063511 (2007). arXiv:0706.1057

    Article  ADS  MathSciNet  Google Scholar 

  93. M. Bojowald, R. Tavakol, Phys. Rev. D 78, 023515 (2008). arXiv:0803.4484

    Article  ADS  MathSciNet  Google Scholar 

  94. M. Bojowald, D. Mulryne, W. Nelson, R. Tavakol, Phys. Rev. D 82, 124055 (2010). arXiv:1004.3979

    Article  ADS  Google Scholar 

  95. M. Bojowald, B. Sandhöfer, A. Skirzewski, A. Tsobanjan, Rev. Math. Phys. 21, 111 (2009). arXiv:0804.3365

    Article  MathSciNet  Google Scholar 

  96. M. Bojowald, A. Tsobanjan, Class. Quantum Gravity 27, 145004 (2010). arXiv:0911.4950

    Article  ADS  MathSciNet  Google Scholar 

  97. R.M. Wald, Phys. Rev. D 48, 2377 (1993). gr-qc/9305024

    Article  ADS  MathSciNet  Google Scholar 

  98. T. Thiemann, Class. Quantum Gravity 23, 2211 (2006). gr-qc/0305080

    Article  ADS  MathSciNet  Google Scholar 

  99. B. Dittrich, T. Thiemann, Class. Quantum Gravity 23, 1025 (2006). gr-qc/0411138

    Article  ADS  MathSciNet  Google Scholar 

  100. A. Higuchi, R.M. Wald, Phys. Rev. D 51, 544 (1995). gr-qc/9407038

    Article  ADS  MathSciNet  Google Scholar 

  101. M. Bojowald, Gen. Relativ. Gravit. 35, 1877 (2003). gr-qc/0305069

    Article  ADS  MathSciNet  Google Scholar 

  102. J. Mielczarek, W. Piechocki, Phys. Rev. D 83, 104003 (2011). arXiv:1011.3418

    Article  ADS  Google Scholar 

  103. R. Helling, arXiv:0912.3011

  104. J. Haro, E. Elizalde, arXiv:0901.2861

  105. M. Bojowald, Proc. R. Soc. A 464, 2135 (2008). arXiv:0710.4919

    Article  ADS  MathSciNet  Google Scholar 

  106. W. Kaminski, T. Pawłowski, Phys. Rev. D 81, 084027 (2010). arXiv:1001.2663

    Article  ADS  Google Scholar 

  107. M. Bojowald, Nat. Phys. 3, 523 (2007)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by NSF grant PHY0748336.

Author information

Authors and Affiliations

  1. The Pennsylvania State University, 104 Davey Lab, University Park, PA, 16802, USA

    Martin Bojowald

Authors
  1. Martin Bojowald
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Martin Bojowald .

Editor information

Editors and Affiliations

  1. CSIC, Instituto de Estructura de la Materia, Madrid, Spain

    Gianluca Calcagni

  2. Department of Physics, National Technical University of Athens, Athens, 15780, Greece

    Lefteris Papantonopoulos

  3. Department of Physics and Astronomy, The University of Tennessee, Nielsen Physics Building 210, Knoxville, 37996-1200, Tennessee, USA

    George Siopsis

  4. Crete Center for Theoretical Physics, Department of Physics, University of Crete, Physics Bldg. 203, Heraklion, 71003, Greece

    Nikos Tsamis

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Bojowald, M. (2013). Loop Quantum Cosmology, Space-Time Structure, and Falsifiability. In: Calcagni, G., Papantonopoulos, L., Siopsis, G., Tsamis, N. (eds) Quantum Gravity and Quantum Cosmology. Lecture Notes in Physics, vol 863. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33036-0_7

Download citation

Publish with us

Policies and ethics

Search

Navigation