Skip to main content
SpringerLink
Log in

Four-fermion interaction from torsion as dark energy

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

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.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Popławski N.J.: Ann. Phys. (Berlin) 523, 291 (2011)

    Article  ADS  Google Scholar 

  2. Kibble T.W.B.: J. Math. Phys. (N.Y.) 2, 212 (1961)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Sciama D.W.: Recent Developments in General Relativity, pp. 415. Pergamon, Oxford (1962)

    Google Scholar 

  4. Sciama D.W.: Rev. Mod. Phys. 36, 463 (1964)

    Article  ADS  Google Scholar 

  5. Sciama D.W.: Rev. Mod. Phys. 36, 1103(E) (1964)

    ADS  Google Scholar 

  6. Lord E.A.: Tensors, Relativity and Cosmology. McGraw-Hill, New Delhi (1976)

    Google Scholar 

  7. Hehl F.W.: Phys. Lett. A 36, 225 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  8. Hehl F.W.: Gen. Relativ. Gravit. 4, 333 (1973)

    Article  MathSciNet  ADS  Google Scholar 

  9. Hehl F.W.: Gen. Relativ. Gravit. 5, 491 (1974)

    Article  MathSciNet  ADS  Google Scholar 

  10. Hehl F.W., von der Heyde P., Kerlick G.D., Nester J.M.: Rev. Mod. Phys. 48, 393 (1976)

    Article  ADS  Google Scholar 

  11. de Sabbata V., Sivaram C.: Spin and Torsion in Gravitation. World Scientific, Singapore (1994)

    Book  MATH  Google Scholar 

  12. Shapiro I.L.: Phys. Rep. 357, 113 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Hammond R.T.: Rep. Prog. Phys. 65, 599 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  14. Popławski N.J.: arXiv:0911.0334

  15. Hehl F.W., Datta B.K.: J. Math. Phys. (N.Y.) 12, 1334 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  16. Heisenberg W.: Rev. Mod. Phys. 29, 269 (1957)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Ivanenko D.D.: Introduction to Nonlinear Quantum Field Theory. Foreign Literature, Moscow (1959)

    Google Scholar 

  18. Isham C.J., Salam A., Strathdee J.: Nature. Phys. Sci. 244, 82 (1973)

    ADS  Google Scholar 

  19. Kerlick G.D.: Phys. Rev. D. 12, 3004 (1975)

    Article  ADS  Google Scholar 

  20. de Sabbata V., Sivaram C.: Astrophys. Space Sci. 165, 51 (1990)

    Article  ADS  Google Scholar 

  21. Shifman M.A., Vainshtein A.I., Zakharov V.I.: Nucl. Phys. B 147, 385 (1979)

    Article  ADS  Google Scholar 

  22. Kolb E.W., Turner M.S.: The Early Universe. Addison-Wesley, New York (1990)

    MATH  Google Scholar 

  23. Alexander S., Biswas T., Calcagni G.: Phys. Rev. D 81, 043511 (2010)

    Article  ADS  Google Scholar 

  24. Alexander S., Biswas T., Calcagni G.: Phys. Rev. D 81, 069902(E) (2010)

    ADS  Google Scholar 

  25. Alexander S., Biswas T.: Phys. Rev. D 80, 023501 (2009)

    Article  ADS  Google Scholar 

  26. Hehl F.W., von der Heyde P., Kerlick G.D.: Phys. Rev. D 10, 1066 (1974)

    Article  MathSciNet  ADS  Google Scholar 

  27. Kuchowicz B.: Gen. Relativ. Gravit. 9, 511 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  28. Gasperini M.: Phys. Rev. Lett. 56, 2873 (1986)

    Article  ADS  Google Scholar 

  29. Popławski N.J.: Phys. Lett. B 694, 181 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  30. Popławski N.J.: Phys. Lett. B 701, 672(E) (2011)

    ADS  Google Scholar 

  31. Peskin M.E., Schroeder D.V.: An Introduction to Quantum Field Theory. Perseus Books, Cambridge, Massachusetts (1995)

    Google Scholar 

  32. Brodsky S.J., de Teramond G.F., Shrock R.: AIP Conf. Proc. 1056, 3 (2008)

    Article  ADS  Google Scholar 

  33. Brodsky S.J., Shrock R.: Proc. Natl. Acad. Sci. 108, 45 (2011)

    Article  ADS  Google Scholar 

  34. Zel’dovich Y.B.: J. Exp. Theor. Phys. Lett. 6, 316 (1967)

    Google Scholar 

  35. Bjorken, J.D.: arXiv:1008.0033

  36. Holst S.: Phys. Rev. D 53, 5966 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  37. Banerjee K.: Class. Quant. Grav. 27, 135012 (2010)

    Article  ADS  Google Scholar 

  38. Barbero J.F.G.: Phys. Rev. D 51, 5507 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  39. Immirzi G.: Class. Quant. Grav. 14, L177 (1997)

    Article  MathSciNet  ADS  Google Scholar 

  40. Perez A., Rovelli C.: Phys. Rev. D 73, 044013 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  41. Freidel L., Minic D., Takeuchi T.: Phys. Rev. D 72, 104002 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  42. Landau L.D., Lifshitz E. M.: The Classical Theory of Fields. Pergamon, Oxford (1975)

    Google Scholar 

  43. Nomura K., Shirafuji T., Hayashi K.: Prog. Theor. Phys. 86, 1239 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  44. Kopczyński W.: Phys. Lett. A 39, 219 (1972)

    Article  ADS  Google Scholar 

  45. Kopczyński W.: Phys. Lett. A 43, 63 (1973)

    Article  ADS  Google Scholar 

  46. Trautman A.: Nature. Phys. Sci. 242, 7 (1973)

    ADS  Google Scholar 

  47. Tafel J.: Phys. Lett. A 45, 341 (1973)

    Article  ADS  Google Scholar 

  48. Hoyle F.: Mon. Not. R. Astron. Soc. 108, 372 (1948)

    ADS  MATH  Google Scholar 

  49. Hoyle F.: Mon. Not. R. Astron. Soc. 109, 365 (1949)

    ADS  MATH  Google Scholar 

  50. Popławski N.J.: Phys. Lett. B 690, 73 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  51. van der Merve P. du T.: Nuovo Cimento Soc. Ital. Fis. A 46, 1 (1978)

    ADS  Google Scholar 

  52. van der Merve P. du T.: Phys. Rev. D 19, 1746 (1979)

    Article  ADS  Google Scholar 

  53. van der Merve P. du T.: Nuovo Cimento Soc. Ital. Fis. A 59, 344 (1980)

    Article  ADS  Google Scholar 

  54. Buchbinder I.L., Odintsov S.D., Shapiro I.L.: Phys. Lett B 162, 92 (1985)

    Article  ADS  Google Scholar 

  55. Popławski N.J.: Phys. Rev. D 83, 084033 (2011)

    Article  ADS  Google Scholar 

  56. Buchbinder I.L., Odintsov S.D., Shapiro I.L.: Effective Action in Quantum Gravity. Taylor and Francis, New York (1992)

    Google Scholar 

  57. Cai Y.-F., Wang J.: Class. Quant. Grav. 25, 165014 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  58. Alford M.: Ann. Rev. Nucl. Part. Sci. 51, 131 (2001)

    Article  ADS  Google Scholar 

  59. Jiang W.Z., Qiu X.J., Zhu Z.Y., He Z.J.: Phys. Rev. C 65, 015210 (2001)

    Article  ADS  Google Scholar 

  60. Mercuri S.: Phys. Rev. D 73, 084016 (2006)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Indiana University, Swain Hall West, 727 East Third Street, Bloomington, IN, 47405, USA

    Nikodem J. Popławski

Authors
  1. Nikodem J. Popławski
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikodem J. Popławski.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Popławski, N.J. Four-fermion interaction from torsion as dark energy. Gen Relativ Gravit 44, 491–499 (2012). https://doi.org/10.1007/s10714-011-1288-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-011-1288-1

Keywords

Search

Navigation