Advertisement

General Relativity and Gravitation

, Volume 40, Issue 2–3, pp 639–660 | Cite as

The dark side of a patchwork universe

  • Martin BojowaldEmail author
Research Article

Abstract

While observational cosmology has recently progressed fast, it revealed a serious dilemma called dark energy: an unknown source of exotic energy with negative pressure driving a current accelerating phase of the universe. All attempts so far to find a convincing theoretical explanation have failed, so that one of the last hopes is the yet to be developed quantum theory of gravity. In this article, loop quantum gravity is considered as a candidate, with an emphasis on properties which might play a role for the dark energy problem. Its basic feature is the discrete structure of space, often associated with quantum theories of gravity on general grounds. This gives rise to well-defined matter Hamiltonian operators and thus sheds light on conceptual questions related to the cosmological constant problem. It also implies typical quantum geometry effects which, from a more phenomenological point of view, may result in dark energy. In particular the latter scenario allows several non-trivial tests which can be made more precise by detailed observations in combination with a quantitative study of numerical quantum gravity. If the speculative possibility of a loop quantum gravitational origin of dark energy turns out to be realized, a program as outlined here will help to hammer out our ideas for a quantum theory of gravity, and at the same time allow predictions for the distant future of our universe.

Keywords

Dark Energy Quantum Gravity Quantum Correction Vacuum Energy Black Hole Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Leibundgut, B.: This volume (2007)Google Scholar
  2. 2.
    Nichols, B.: This volume (2007)Google Scholar
  3. 3.
    Sarkar, S.: This volume (2007)Google Scholar
  4. 4.
    Alexander, S., Vaid, D.: A fine tuning free resolution of the cosmological constant problem. hep-th/0702064 (2007)Google Scholar
  5. 5.
    Arnowitt R., Deser S. and Misner C.W. (1962). The Dynamics of General Relativity. Wiley, New York Google Scholar
  6. 6.
    Ashtekar A. (1987). New hamiltonian formulation of general relativity. Phys. Rev. D 36(6): 1587–1602 CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Ashtekar A., Baez J.C., Corichi A. and Krasnov K. (1998). Quantum geometry and black hole entropy. Phys. Rev. Lett. 80: 904–907 zbMATHCrossRefADSMathSciNetGoogle Scholar
  8. 8.
    Ashtekar A., Baez J.C. and Krasnov K. (2000). Quantum geometry of isolated horizons and black hole entropy. Adv. Theor. Math. Phys. 4: 1–94 zbMATHMathSciNetGoogle Scholar
  9. 9.
    Ashtekar A., Bojowald M. and Lewandowski J. (2003). Mathematical structure of loop quantum cosmology. Adv. Theor. Math. Phys. 7: 233–268 MathSciNetGoogle Scholar
  10. 10.
    Ashtekar A. and Lewandowski J. (1997). Quantum theory of geometry I: Area operators. Class. Quantum Grav. 14: A55–A82 zbMATHCrossRefADSMathSciNetGoogle Scholar
  11. 11.
    Ashtekar A. and Lewandowski J. (1997). Quantum theory of geometry II: Volume operators. Adv. Theor. Math. Phys. 1: 388–429 zbMATHMathSciNetGoogle Scholar
  12. 12.
    Ashtekar A. and Lewandowski J. (2004). Background independent quantum gravity: a status report. Class. Quantum Grav. 21: R53–R152 zbMATHCrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Ashtekar A., Lewandowski J., Marolf D., Mourão J. and Thiemann T. (1995). Quantization of diffeomorphism invariant theories of connections with local degrees of freedom. J. Math. Phys. 36(11): 6456–6493 zbMATHCrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Ashtekar A., Pawlowski T. and Singh P. (2006). Quantum nature of the big bang: an analytical and numerical investigation. Phys. Rev. D 73: 124038 CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    Ashtekar A., Pawlowski T. and Singh P. (2006). Quantum nature of the big bang: improved dynamics. Phys. Rev. D 74: 084003 CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Barbero J.F. (1995). Real ashtekar variables for lorentzian signature space-times. Phys. Rev. D 51(10): 5507–5510 CrossRefADSMathSciNetGoogle Scholar
  17. 17.
    Bergmann P.G. (1961). Observables in general relativity. Rev. Mod. Phys. 33: 510–514 zbMATHCrossRefADSMathSciNetGoogle Scholar
  18. 18.
    Bilson-Thompson, O., Markopoulou, F., Smolin, L.: Quantum gravity and the standard model. hep-th/0603022 (2006)Google Scholar
  19. 19.
    Bojowald M. (2001). Absence of a singularity in loop quantum cosmology. Phys. Rev. Lett. 86: 5227–5230 CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    Bojowald M. (2001). Inverse scale factor in isotropic quantum geometry. Phys. Rev. D 64: 084018 CrossRefADSMathSciNetGoogle Scholar
  21. 21.
    Bojowald M. (2002). Inflation from quantum geometry. Phys. Rev. Lett. 89: 261301 CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    Bojowald M. (2002). Isotropic loop quantum cosmology. Class. Quantum Grav 19: 2717–2741 zbMATHCrossRefADSMathSciNetGoogle Scholar
  23. 23.
    Bojowald M. (2002). Quantization ambiguities in isotropic quantum geometry. Class. Quantum Grav. 19: 5113–5130 zbMATHCrossRefADSMathSciNetGoogle Scholar
  24. 24.
    Bojowald, M.: Loop quantum cosmology: recent progress. In: Proceedings of the International Conference on Gravitation and Cosmology (ICGC 2004), Cochin, India. Pramana 63, 765–776, 2004Google Scholar
  25. 25.
    Bojowald, M.: Loop quantum cosmology. Living Rev. Relativity, 8:11 (2005) http://relativity.livingreviews.org/Articles/lrr-2005-11/ Google Scholar
  26. 26.
    Bojowald M. (2005). Non-singular black holes and degrees of freedom in quantum gravity. Phys. Rev. Lett. 95: 061301 CrossRefADSMathSciNetGoogle Scholar
  27. 27.
    Bojowald M. (2006). Degenerate configurations, singularities and the non-abelian nature of loop quantum gravity. Class. Quantum Grav. 23: 987–1008 zbMATHCrossRefADSMathSciNetGoogle Scholar
  28. 28.
    Bojowald M. (2006). Loop quantum cosmology and inhomogeneities. Gen. Rel. Grav. 38: 1771–1795 zbMATHCrossRefADSMathSciNetGoogle Scholar
  29. 29.
    Bojowald, M.: Quantum gravity and cosmological observations. In Proceedings of the VIth Latin American Symposium on High Energy Physics (Puerto Vallarta, Mexico). AIP Conf. Proc. 917, 130–137 (2007)Google Scholar
  30. 30.
    Bojowald, M.: Singularities and quantum gravity. In: Proceedings of the XIIth Brazilian School on Cosmology and Gravitation. AIP Conf. Proc. 910, 294–333 (2007)Google Scholar
  31. 31.
    Bojowald M., Cartin D. and Khanna G. (2007). Lattice refining loop quantum cosmology, anisotropic models and stability. Phys. Rev. D 76: 64018 CrossRefADSGoogle Scholar
  32. 32.
    Bojowald M. and Das R. (2007). The radiation equation of state and loop quantum gravity corrections. Phys. Rev. D 75: 123521 CrossRefADSMathSciNetGoogle Scholar
  33. 33.
    Bojowald, M., Das, R., Scherrer, R.: arXiv:0710.5734 (2007)Google Scholar
  34. 34.
    Bojowald M., Hernández H., Kagan M., Singh P. and Skirzewski A. (2007). Formation and evolution of structure in loop cosmology. Phys. Rev. Lett. 98: 031301 CrossRefADSMathSciNetGoogle Scholar
  35. 35.
    Bojowald M., Hernández H., Kagan M. and Skirzewski A. (2007). Effective constraints of loop quantum gravity. Phys. Rev. D 75: 064022 CrossRefADSMathSciNetGoogle Scholar
  36. 36.
    Bojowald M. and Kastrup H.A. (2000). Symmetry reduction for quantized diffeomorphism invariant theories of connections. Class. Quantum Grav. 17: 3009–3043 zbMATHCrossRefADSMathSciNetGoogle Scholar
  37. 37.
    Bojowald M., Lidsey J.E., Mulryne D.J., Singh P. and Tavakol R. (2004). Inflationary cosmology and quantization ambiguities in semi-classical loop quantum gravity. Phys. Rev. D 70: 043530 CrossRefADSMathSciNetGoogle Scholar
  38. 38.
    Bojowald M., Singh P. and Skirzewski A. (2004). Coordinate time dependence in quantum gravity. Phys. Rev. D 70: 124022 CrossRefADSMathSciNetGoogle Scholar
  39. 39.
    Bojowald M. and Skirzewski A. (2006). Effective equations of motion for quantum systems. Rev. Math. Phys. 18: 713–745 zbMATHCrossRefMathSciNetGoogle Scholar
  40. 40.
    Bojowald, M., Skirzewski, A.: Quantum gravity and higher curvature actions. In: Current Mathematical Topics in Gravitation and Cosmology (42nd Karpacz Winter School of Theoretical Physics). Int. J. Geom. Meth. Mod. Phys. 4, 25–52 (2007)Google Scholar
  41. 41.
    Copeland E.J., Lidsey J.E. and Mizuno S. (2006). Correspondence between loop-inspired and braneworld cosmology. Phys. Rev. D 73: 043503 CrossRefADSMathSciNetGoogle Scholar
  42. 42.
    Date G. and Hossain G.M. (2005). Genericity of inflation in isotropic loop quantum cosmology. Phys. Rev. Lett. 94: 011301 CrossRefADSMathSciNetGoogle Scholar
  43. 43.
    Dittrich, B.: Aspects of Classical and Quantum Dynamics of Canonical General Relativity. Ph.D. thesis, University of Potsdam (2005)Google Scholar
  44. 44.
    Dittrich B. (2006). Partial and complete observables for hamiltonian constrained systems. Class. Quantum Grav. 23: 6155–6184 zbMATHCrossRefADSMathSciNetGoogle Scholar
  45. 45.
    Domagala M. and Lewandowski J. (2004). Black hole entropy from quantum geometry. Class. Quantum Grav. 21: 5233–5243 zbMATHCrossRefADSMathSciNetGoogle Scholar
  46. 46.
    Engle J. (2006). Quantum field theory and its symmetry reduction. Class. Quant. Grav. 23: 2861–2893 zbMATHCrossRefADSMathSciNetGoogle Scholar
  47. 47.
    Engle, J.: On the physical interpretation of states in loop quantum cosmology. gr-qc/0701132 (2007)Google Scholar
  48. 48.
    Freidel L., Minic D. and Takeuchi T. (2005). Quantum gravity, torsion, parity violation and all that. Phys. Rev. D 72: 104002 CrossRefADSMathSciNetGoogle Scholar
  49. 49.
    Giesel K. and Thiemann T. (2007). Algebraic quantum gravity (AQG) I. Conceptual setup. Class. Quantum Grav. 24: 2465–2497 zbMATHCrossRefADSMathSciNetGoogle Scholar
  50. 50.
    Immirzi G. (1997). Real and complex connections for canonical gravity. Class. Quantum Grav. 14: L177–L181 CrossRefADSMathSciNetGoogle Scholar
  51. 51.
    Koslowski, T.: Reduction of a quantum theory. gr-qc/0612138 (2006)Google Scholar
  52. 52.
    Koslowski, T.: A cosmological sector in loop quantum gravity. arXiv:0711.1098 (2007)Google Scholar
  53. 53.
    Lidsey J.E. (2004). Early universe dynamics in semi-classical loop quantum cosmology. JCAP 0412: 007 ADSMathSciNetGoogle Scholar
  54. 54.
    Mathur S. (2003). How does the universe expand?. Int. J. Mod. Phys. D 12: 1681–1686 CrossRefADSMathSciNetGoogle Scholar
  55. 55.
    Meissner K.A. (2004). Black hole entropy in loop quantum gravity. Class. Quantum Grav. 21: 5245–5251 zbMATHCrossRefADSMathSciNetGoogle Scholar
  56. 56.
    Mercuri S. (2006). Fermions in Ashtekar–Barbero connections formalism for arbitrary values of the immirzi parameter. Phys. Rev. D 73: 084016 CrossRefADSMathSciNetGoogle Scholar
  57. 57.
    Perez A. and Rovelli C. (2006). Physical effects of the immirzi parameter. Phys. Rev. D 73: 044013 CrossRefADSMathSciNetGoogle Scholar
  58. 58.
    Rovelli C. (1991). Quantum reference systems. Class. Quantum Grav. 8: 317–332 CrossRefADSMathSciNetGoogle Scholar
  59. 59.
    Rovelli C. (1991). What is observable in classical and quantum gravity?. Class. Quantum Grav. 8: 297–316 CrossRefADSMathSciNetGoogle Scholar
  60. 60.
    Rovelli C. (2004). Quantum Gravity. Cambridge University Press, Cambridge, UK zbMATHGoogle Scholar
  61. 61.
    Rovelli C. and Smolin L. (1994). The physical hamiltonian in nonperturbative quantum gravity. Phys. Rev. Lett. 72: 446–449 zbMATHCrossRefADSMathSciNetGoogle Scholar
  62. 62.
    Rovelli, C., Smolin, L.: Discreteness of area and volume in quantum gravity. Nucl. Phys. B 442, 593–619 (1995). Erratum: Nucl. Phys. B 456, 753 (1995)Google Scholar
  63. 63.
    Rovelli C. and Smolin L. (1995). Spin networks and quantum gravity. Phys. Rev. D 52(10): 5743–5759 CrossRefMathSciNetGoogle Scholar
  64. 64.
    Sahlmann H. and Thiemann T. (2006). Towards the QFT on curved spacetime limit of QGR. I: A general scheme. Class. Quantum Grav. 23: 867–908 zbMATHCrossRefADSMathSciNetGoogle Scholar
  65. 65.
    Sahlmann H. and Thiemann T. (2006). Towards the QFT on curved spacetime limit of QGR. II: A concrete implementation. Class. Quantum Grav. 23: 909–954 zbMATHCrossRefADSMathSciNetGoogle Scholar
  66. 66.
    Samart D. and Gumjudpai B. (2007). Phantom field dynamics in loop quantum cosmology. Phys. Rev. D 76: 043514 CrossRefADSMathSciNetGoogle Scholar
  67. 67.
    Sami M., Singh P. and Tsujikawa S. (2006). Avoidance of future singularities in loop quantum cosmology. Phys. Rev. D 74: 043514 CrossRefADSMathSciNetGoogle Scholar
  68. 68.
    Singh P. (2006). Loop cosmological dynamics and dualities with randall-sundrum braneworlds. Phys. Rev. D 73: 063508 CrossRefADSMathSciNetGoogle Scholar
  69. 69.
    Skirzewski, A.: Effective Equations of Motion for Quantum Systems. Ph.D. thesis, Humboldt-Universität Berlin (2006)Google Scholar
  70. 70.
    Thiemann T. (1998). Quantum spin dynamics (QSD). Class. Quantum Grav. 15: 839–873 zbMATHCrossRefADSMathSciNetGoogle Scholar
  71. 71.
    Thiemann T. (1998). QSD V: Quantum gravity as the natural regulator of matter quantum field theories. Class. Quantum Grav. 15: 1281–1314 zbMATHCrossRefADSMathSciNetGoogle Scholar
  72. 72.
    Thiemann, T.: Introduction to modern canonical quantum general relativity. gr-qc/0110034 (2001)Google Scholar
  73. 73.
    Tsujikawa S., Singh P. and Maartens R. (2004). Loop quantum gravity effects on inflation and the cmb. Class. Quantum Grav. 21: 5767–5775 zbMATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Institute for Gravitational Physics and GeometryThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations