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JETP Letters

, Volume 91, Issue 6, pp 259–265 | Cite as

Towards a solution of the cosmological constant problem

  • F. R. Klinkhamer
  • G. E. Volovik
Gravity, Astrophysics

Abstract

The standard model of elementary particle physics and the theory of general relativity can be extended by the introduction of a vacuum variable which is responsible for the near vanishing of the present cosmological constant (vacuum energy density). The explicit realization of this vacuum variable can be via a three-form gauge field, an aether-type velocity field, or any other field appropriate for the description of the equilibrium state corresponding to the Lorentz-invariant quantum vacuum. The extended theory has, without fine-tuning, a Minkowski-type solution of the field equations with spacetime-independent fields and provides, therefore, a possible solution of the main cosmological constant problem.

Keywords

JETP Letter Minkowski Spacetime Energy Momentum Tensor Vacuum Energy Density Elementary Particle Physic 
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.

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References

  1. 1.
    S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).zbMATHMathSciNetADSCrossRefGoogle Scholar
  2. 2.
    S. Weinberg, in Critical Dialogues in Cosmology, Ed. by N. Turok (World Sci., Singapore, 1997), p. 195; arXiv:astro-ph/9610044.Google Scholar
  3. 3.
    F. R. Klinkhamer and G. E. Volovik, Phys. Rev. D 77, 085015 (2008); arXiv:0711.3170.ADSCrossRefGoogle Scholar
  4. 4.
    F. R. Klinkhamer and G. E. Volovik, Phys. Rev. D 78, 063528 (2008); arXiv:0806.2805.ADSCrossRefGoogle Scholar
  5. 5.
    F. R. Klinkhamer and G. E. Volovik, Phys. Rev. D 80, 083001 (2009); arXiv:0905.1919.ADSCrossRefGoogle Scholar
  6. 6.
    M. J. Duff and P. van Nieuwenhuizen, Phys. Lett. B 94, 179 (1980).ADSCrossRefGoogle Scholar
  7. 7.
    A. Aurilia, H. Nicolai, and P. K. Townsend, Nucl. Phys. B 176, 509 (1980).MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    S. W. Hawking, Phys. Lett. B 134, 403 (1984).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    M. Henneaux and C. Teitelboim, Phys. Lett. B 143, 415 (1984).MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    M. J. Duff, Phys. Lett. B 226, 36 (1989).MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    M. J. Duncan and L. G. Jensen, Nucl. Phys. B 336, 100 (1990).MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    R. Bousso and J. Polchinski, JHEP 0006, 006 (2000); arXiv:hep-th/0004134.MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    A. Aurilia and E. Spallucci, Phys. Rev. D 69, 105004 (2004); arXiv:hep-th/0402096.MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Z. C. Wu, Phys. Lett. B 659, 891 (2008); arXiv:0709.3314.MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    M. Veltman, Diagrammatica: The Path to Feynman Rules (Cambridge Univ., Cambridge, England, 1994), Appendix E.Google Scholar
  16. 16.
    N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge Univ., Cambridge, England, 1982).zbMATHGoogle Scholar
  17. 17.
    C. Brans and R. H. Dicke, Phys. Rev. 124, 925 (1961).zbMATHMathSciNetADSCrossRefGoogle Scholar
  18. 18.
    A. A. Starobinsky, Phys. Lett. B 91, 99 (1980).ADSCrossRefGoogle Scholar
  19. 19.
    W. Hu and I. Sawicki, Phys. Rev. D 76, 064004 (2007); arXiv:0705.1158.ADSCrossRefGoogle Scholar
  20. 20.
    S. A. Appleby and R. A. Battye, Phys. Lett. B 654, 7 (2007); arXiv:0705.3199.MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    A. A. Starobinsky, JETP Lett. 86, 157 (2007); arXiv:0706.2041.ADSCrossRefGoogle Scholar
  22. 22.
    P. Brax, C. van de Bruck, A. C. Davis, and D. J. Shaw, Phys. Rev. D 78, 104021 (2008); arXiv:0806.3415.MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    F. R. Klinkhamer and G. E. Volovik, JETP Lett. 88, 289 (2008); arXiv:0807.3896.ADSCrossRefGoogle Scholar
  24. 24.
    F. R. Klinkhamer and G. E. Volovik, Phys. Rev. D 79, 063527 (2009); arXiv:0811.4347.ADSCrossRefGoogle Scholar
  25. 25.
    F. R. Klinkhamer, Phys. Rev. D 81, 043006 (2010), arXiv:0904.3276.ADSCrossRefGoogle Scholar
  26. 26.
    There is no need, here, to dwell on the interpretation of μ0 as a chemical potential [3, 4]. Still, it may be relevant for the future development of the theory that the obtained vacuum can be viewed as a self-sustained system existing at zero external pressure, P ext = 0, and that Eq. (8b) can be read as the integrated form of the thermodynamic Gibbs-Duhem equation, −P = ε −μq, provided the identification μ = dε/dq and the pressure-equilibrium condition P = P ext = 0 hold.Google Scholar
  27. 27.
    A. D. Dolgov, JETP Lett. 41, 345 (1985).ADSGoogle Scholar
  28. 28.
    A. D. Dolgov, Phys. Rev. D 55, 5881 (1997); arXiv:astro-ph/9608175.ADSCrossRefGoogle Scholar
  29. 29.
    A. M. Polyakov, Mod. Phys. Lett. A 6, 635 (1991); I. Klebanov and A. M. Polyakov, Mod. Phys. Lett. A 6, 3273 (1991); arXiv:hep-th/9109032.zbMATHMathSciNetADSCrossRefGoogle Scholar
  30. 30.
    A. M. Polyakov, private communication.Google Scholar
  31. 31.
    A. I. Larkin and S. A. Pikin, Sov. Phys. JETP 29, 891 (1969); J. Sak, Phys. Rev. B 10, 3957 (1974).ADSGoogle Scholar
  32. 32.
    T. Jacobson, in Proceedings of the Conference From Quantum to Emergent Gravity: Theory and Phenomenology, PoS QG-PH, 020 (2007); arXiv:0801.1547.Google Scholar
  33. 33.
    V. A. Rubakov and P. G. Tinyakov, Phys. Rev. D 61, 087503 (2000); arXiv:hep-ph/9906239.MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    J. Khoury and A. Weltman, Phys. Rev. D 69, 044026 (2004); arXiv:astro-ph/0309411.MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    The general term “quintessence” from [36] has, over the years, become associated with a fundamental scalar field and the use of the slightly different term “quinta essential“ for the vacuum field q is to avoid any possible misunderstanding.Google Scholar
  36. 36.
    R. R. Caldwell, R. Dave, and P. J. Steinhardt, Phys. Rev. Lett. 80, 1582 (1998); arXiv:astro-ph/9708069.ADSCrossRefGoogle Scholar
  37. 37.
    J. J. van der Bij, H. van Dam, and Y. J. Ng, Physica A 116, 307 (1982).MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    L. Smolin, Phys. Rev. D 80, 084003 (2009); arXiv:0904.4841.MathSciNetADSCrossRefGoogle Scholar
  39. 39.
    As to the terminology of “main“ cosmological constant problem, we refer to the required cancellation of a huge initial contribution to the gravitating vacuum energy density which is of the order of (E ew)4 or more; see also the discussion under Eq. (3).Google Scholar
  40. 40.
    A. G. Riess et al. (Supernova Search Team Collab.), Astron. J. 116, 1009 (1998); arXiv:astro-ph/9805201.ADSCrossRefGoogle Scholar
  41. 41.
    S. Perlmutter et al. (Supernova Cosmology Project Collab.), Astrophys. J. 517, 565 (1999); arXiv:astro-ph/9812133.ADSCrossRefGoogle Scholar
  42. 42.
    E. Komatsu et al., Astrophys. J. Suppl. 180, 330 (2009); arXiv:0803.0547.ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Institute for Theoretical PhysicsUniversity of Karlsruhe, Karlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.Low Temperature LaboratoryAalto UniversityAALTOFinland
  3. 3.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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