General Relativity and Gravitation

, Volume 44, Issue 2, pp 491–499 | Cite as

Four-fermion interaction from torsion as dark energy

Research Article

Abstract

The observed small, positive cosmological constant may originate from a four-fermion interaction generated by the spin-torsion coupling in the Einstein–Cartan–Sciama–Kibble gravity if the fermions are condensing. In particular, such a condensation occurs for quark fields during the quark-gluon/hadron phase transition in the early Universe. We study how the torsion-induced four-fermion interaction is affected by adding two terms to the Dirac Lagrangian density: the parity-violating pseudoscalar density dual to the curvature tensor and a spinor-bilinear scalar density which measures the nonminimal coupling of fermions to torsion.

Keywords

Einstein–Cartan–Sciama–Kibble gravity Torsion Spin Dirac Lagrangian Hehl–Datta equation Four-fermion interaction Cosmological constant Quark condensate Parity Nonminimal coupling 

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References

  1. 1.
    Popławski N.J.: Ann. Phys. (Berlin) 523, 291 (2011)ADSCrossRefGoogle Scholar
  2. 2.
    Kibble T.W.B.: J. Math. Phys. (N.Y.) 2, 212 (1961)MathSciNetADSMATHCrossRefGoogle Scholar
  3. 3.
    Sciama D.W.: Recent Developments in General Relativity, pp. 415. Pergamon, Oxford (1962)Google Scholar
  4. 4.
    Sciama D.W.: Rev. Mod. Phys. 36, 463 (1964)ADSCrossRefGoogle Scholar
  5. 5.
    Sciama D.W.: Rev. Mod. Phys. 36, 1103(E) (1964)ADSGoogle Scholar
  6. 6.
    Lord E.A.: Tensors, Relativity and Cosmology. McGraw-Hill, New Delhi (1976)Google Scholar
  7. 7.
    Hehl F.W.: Phys. Lett. A 36, 225 (1971)MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Hehl F.W.: Gen. Relativ. Gravit. 4, 333 (1973)MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Hehl F.W.: Gen. Relativ. Gravit. 5, 491 (1974)MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Hehl F.W., von der Heyde P., Kerlick G.D., Nester J.M.: Rev. Mod. Phys. 48, 393 (1976)ADSCrossRefGoogle Scholar
  11. 11.
    de Sabbata V., Sivaram C.: Spin and Torsion in Gravitation. World Scientific, Singapore (1994)MATHCrossRefGoogle Scholar
  12. 12.
    Shapiro I.L.: Phys. Rep. 357, 113 (2002)MathSciNetADSMATHCrossRefGoogle Scholar
  13. 13.
    Hammond R.T.: Rep. Prog. Phys. 65, 599 (2002)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Popławski N.J.: arXiv:0911.0334Google Scholar
  15. 15.
    Hehl F.W., Datta B.K.: J. Math. Phys. (N.Y.) 12, 1334 (1971)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Heisenberg W.: Rev. Mod. Phys. 29, 269 (1957)MathSciNetADSMATHCrossRefGoogle Scholar
  17. 17.
    Ivanenko D.D.: Introduction to Nonlinear Quantum Field Theory. Foreign Literature, Moscow (1959)Google Scholar
  18. 18.
    Isham C.J., Salam A., Strathdee J.: Nature. Phys. Sci. 244, 82 (1973)ADSGoogle Scholar
  19. 19.
    Kerlick G.D.: Phys. Rev. D. 12, 3004 (1975)ADSCrossRefGoogle Scholar
  20. 20.
    de Sabbata V., Sivaram C.: Astrophys. Space Sci. 165, 51 (1990)ADSCrossRefGoogle Scholar
  21. 21.
    Shifman M.A., Vainshtein A.I., Zakharov V.I.: Nucl. Phys. B 147, 385 (1979)ADSCrossRefGoogle Scholar
  22. 22.
    Kolb E.W., Turner M.S.: The Early Universe. Addison-Wesley, New York (1990)MATHGoogle Scholar
  23. 23.
    Alexander S., Biswas T., Calcagni G.: Phys. Rev. D 81, 043511 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    Alexander S., Biswas T., Calcagni G.: Phys. Rev. D 81, 069902(E) (2010)ADSGoogle Scholar
  25. 25.
    Alexander S., Biswas T.: Phys. Rev. D 80, 023501 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    Hehl F.W., von der Heyde P., Kerlick G.D.: Phys. Rev. D 10, 1066 (1974)MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    Kuchowicz B.: Gen. Relativ. Gravit. 9, 511 (1978)MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    Gasperini M.: Phys. Rev. Lett. 56, 2873 (1986)ADSCrossRefGoogle Scholar
  29. 29.
    Popławski N.J.: Phys. Lett. B 694, 181 (2010)MathSciNetADSCrossRefGoogle Scholar
  30. 30.
    Popławski N.J.: Phys. Lett. B 701, 672(E) (2011)ADSGoogle Scholar
  31. 31.
    Peskin M.E., Schroeder D.V.: An Introduction to Quantum Field Theory. Perseus Books, Cambridge, Massachusetts (1995)Google Scholar
  32. 32.
    Brodsky S.J., de Teramond G.F., Shrock R.: AIP Conf. Proc. 1056, 3 (2008)ADSCrossRefGoogle Scholar
  33. 33.
    Brodsky S.J., Shrock R.: Proc. Natl. Acad. Sci. 108, 45 (2011)ADSCrossRefGoogle Scholar
  34. 34.
    Zel’dovich Y.B.: J. Exp. Theor. Phys. Lett. 6, 316 (1967)Google Scholar
  35. 35.
    Bjorken, J.D.: arXiv:1008.0033Google Scholar
  36. 36.
    Holst S.: Phys. Rev. D 53, 5966 (1996)MathSciNetADSCrossRefGoogle Scholar
  37. 37.
    Banerjee K.: Class. Quant. Grav. 27, 135012 (2010)ADSCrossRefGoogle Scholar
  38. 38.
    Barbero J.F.G.: Phys. Rev. D 51, 5507 (1995)MathSciNetADSCrossRefGoogle Scholar
  39. 39.
    Immirzi G.: Class. Quant. Grav. 14, L177 (1997)MathSciNetADSCrossRefGoogle Scholar
  40. 40.
    Perez A., Rovelli C.: Phys. Rev. D 73, 044013 (2006)MathSciNetADSCrossRefGoogle Scholar
  41. 41.
    Freidel L., Minic D., Takeuchi T.: Phys. Rev. D 72, 104002 (2005)MathSciNetADSCrossRefGoogle Scholar
  42. 42.
    Landau L.D., Lifshitz E. M.: The Classical Theory of Fields. Pergamon, Oxford (1975)Google Scholar
  43. 43.
    Nomura K., Shirafuji T., Hayashi K.: Prog. Theor. Phys. 86, 1239 (1991)MathSciNetADSCrossRefGoogle Scholar
  44. 44.
    Kopczyński W.: Phys. Lett. A 39, 219 (1972)ADSCrossRefGoogle Scholar
  45. 45.
    Kopczyński W.: Phys. Lett. A 43, 63 (1973)ADSCrossRefGoogle Scholar
  46. 46.
    Trautman A.: Nature. Phys. Sci. 242, 7 (1973)ADSGoogle Scholar
  47. 47.
    Tafel J.: Phys. Lett. A 45, 341 (1973)ADSCrossRefGoogle Scholar
  48. 48.
    Hoyle F.: Mon. Not. R. Astron. Soc. 108, 372 (1948)ADSMATHGoogle Scholar
  49. 49.
    Hoyle F.: Mon. Not. R. Astron. Soc. 109, 365 (1949)ADSMATHGoogle Scholar
  50. 50.
    Popławski N.J.: Phys. Lett. B 690, 73 (2010)MathSciNetADSCrossRefGoogle Scholar
  51. 51.
    van der Merve P. du T.: Nuovo Cimento Soc. Ital. Fis. A 46, 1 (1978)ADSGoogle Scholar
  52. 52.
    van der Merve P. du T.: Phys. Rev. D 19, 1746 (1979)ADSCrossRefGoogle Scholar
  53. 53.
    van der Merve P. du T.: Nuovo Cimento Soc. Ital. Fis. A 59, 344 (1980)ADSCrossRefGoogle Scholar
  54. 54.
    Buchbinder I.L., Odintsov S.D., Shapiro I.L.: Phys. Lett B 162, 92 (1985)ADSCrossRefGoogle Scholar
  55. 55.
    Popławski N.J.: Phys. Rev. D 83, 084033 (2011)ADSCrossRefGoogle Scholar
  56. 56.
    Buchbinder I.L., Odintsov S.D., Shapiro I.L.: Effective Action in Quantum Gravity. Taylor and Francis, New York (1992)Google Scholar
  57. 57.
    Cai Y.-F., Wang J.: Class. Quant. Grav. 25, 165014 (2008)MathSciNetADSCrossRefGoogle Scholar
  58. 58.
    Alford M.: Ann. Rev. Nucl. Part. Sci. 51, 131 (2001)ADSCrossRefGoogle Scholar
  59. 59.
    Jiang W.Z., Qiu X.J., Zhu Z.Y., He Z.J.: Phys. Rev. C 65, 015210 (2001)ADSCrossRefGoogle Scholar
  60. 60.
    Mercuri S.: Phys. Rev. D 73, 084016 (2006)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of PhysicsIndiana UniversityBloomingtonUSA

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