International Journal of Theoretical Physics

, Volume 51, Issue 10, pp 3186–3207

A Modified Theory of Gravity with Torsion and Its Applications to Cosmology and Particle Physics

Article

Abstract

In this paper we consider the most general least-order derivative theory of gravity in which not only curvature but also torsion is explicitly present in the Lagrangian, and where all independent fields have their own coupling constant: we will apply this theory to the case of ELKO fields, which is the acronym of the German Eigenspinoren des LadungsKonjugationsOperators designating eigenspinors of the charge conjugation operator, and thus they are a Majorana-like special type of spinors; and to the Dirac fields, the most general type of spinors. We shall see that because torsion has a coupling constant that is still undetermined, the ELKO and Dirac field equations are endowed with self-interactions whose coupling constant is undetermined: we discuss different applications according to the value of the coupling constants and the different properties that consequently follow. We highlight that in this approach, the ELKO and Dirac field’s self-interactions depend on the coupling constant as a parameter that may even make these non-linearities manifest at subatomic scales.

Keywords

Torsion tensor ELKO and Dirac fields 

References

  1. 1.
    Fabbri, L., Vignolo, S.: arXiv:1201.0286 [gr-qc] (2012)
  2. 2.
    Hehl, F.W., Von Der Heyde, P., Kerlick, G.D., Nester, J.M.: Rev. Mod. Phys. 48, 393 (1976) ADSCrossRefGoogle Scholar
  3. 3.
    Hehl, F.W., McCrea, J.D., Mielke, E.W., Ne’eman, Y.: Phys. Rep. 258, 1 (1995) MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Fatibene, L., Francaviglia, M.: Natural and Gauge Natural Formalism for Classical Field Theories. A Geometric Perspective Including Spinors and Gauge Theories. Kluwer Academic, Dordrecht (2003) MATHGoogle Scholar
  5. 5.
    Cianci, R., Vignolo, S., Bruno, D.: J. Phys. A, Math. Gen. 36, 8341 (2003) MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    Vignolo, S., Cianci, R.: J. Math. Phys. 45, 4448 (2004) MathSciNetADSMATHCrossRefGoogle Scholar
  7. 7.
    Vignolo, S., Cianci, R., Bruno, D.: Int. J. Geom. Methods Mod. Phys. 3, 1493 (2006) MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Cianci, R., Vignolo, S.: AIP Conf. Proc. 751, 64 (2005) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Fabbri, L.: Phys. Lett. B 707, 415 (2012) MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Kostelecky, V.A., Russell, N., Tasson, J.: Phys. Rev. Lett. 100, 111102 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    Fabbri, L.: arXiv:1104.5002 [gr-qc] (2011)
  12. 12.
    Fabbri, L., Paranjape, M.B.: Phys. Rev. D 83, 104046 (2011) ADSCrossRefGoogle Scholar
  13. 13.
    Fabbri, L., Paranjape, M.B.: Int. J. Mod. Phys. D 20, 1941 (2011) MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Flanagan, E.E.: Phys. Rev. D 74, 023002 (2006) MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Capozziello, S., Lambiase, G., Stornaiolo, C.: Ann. Phys. 10, 713 (2001) MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Ahluwalia, D.V., Grumiller, D.: J. Cosmol. Astropart. Phys. 0507, 012 (2005) ADSCrossRefGoogle Scholar
  17. 17.
    Ahluwalia, D.V., Grumiller, D.: Phys. Rev. D 72, 067701 (2005) ADSCrossRefGoogle Scholar
  18. 18.
    Ahluwalia, D.V., Lee, C.Y., Schritt, D.: Phys. Lett. B 687, 248 (2010) ADSCrossRefGoogle Scholar
  19. 19.
    Ahluwalia, D.V., Lee, C.Y., Schritt, D.: Phys. Rev. D 83, 065017 (2011) ADSCrossRefGoogle Scholar
  20. 20.
    Boehmer, C.G.: Ann. Phys. 16, 38 (2007) MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Boehmer, C.G.: Ann. Phys. 16, 325 (2007) MATHCrossRefGoogle Scholar
  22. 22.
    Ahluwalia, D.V.: Int. J. Mod. Phys. D 15, 2267 (2006) ADSMATHCrossRefGoogle Scholar
  23. 23.
    Ahluwalia, D.V., Horvath, S.P.: J. High Energy Phys. 1011, 078 (2010) ADSCrossRefGoogle Scholar
  24. 24.
    Böhmer, C.G.: Phys. Rev. D 77, 123535 (2008) ADSCrossRefGoogle Scholar
  25. 25.
    Böhmer, C.G., Mota, D.F.: Phys. Lett. B 663, 168 (2008) ADSCrossRefGoogle Scholar
  26. 26.
    Boehmer, C., Burnett, J.: Phys. Rev. D 78, 104001 (2008) ADSCrossRefGoogle Scholar
  27. 27.
    Boehmer, C., Burnett, J.: Mod. Phys. Lett. A 25, 101 (2010) ADSMATHCrossRefGoogle Scholar
  28. 28.
    Boehmer, C., Burnett, J., Mota, D., Shaw, D.J.: J. High Energy Phys. 1007, 53 (2010) ADSCrossRefGoogle Scholar
  29. 29.
    Shankaranarayanan, S.: Int. J. Mod. Phys. D 18, 2173 (2009) MathSciNetADSMATHCrossRefGoogle Scholar
  30. 30.
    Shankaranarayanan, S.: arXiv:1002.1128 [astro-ph.CO] (2010)
  31. 31.
    da Rocha, R., Rodrigues, W.A.J.: Mod. Phys. Lett. A 21, 65 (2006) ADSMATHCrossRefGoogle Scholar
  32. 32.
    da Rocha, R., Hoff da Silva, J.M.: J. Math. Phys. 48, 123517 (2007) MathSciNetADSCrossRefGoogle Scholar
  33. 33.
    da Rocha, R., Hoff da Silva, J.M.: Adv. Appl. Clifford Algebras 20, 847 (2010) MATHCrossRefGoogle Scholar
  34. 34.
    Hoff da Silva, J., da Rocha, R.: Int. J. Mod. Phys. A 24, 3227 (2009) ADSMATHCrossRefGoogle Scholar
  35. 35.
    Dias, M., de Campos, F., da Silva, J.M.H.: Phys. Lett. B 706, 352 (2012) ADSCrossRefGoogle Scholar
  36. 36.
    da Rocha, R., Bernardini, A.E., da Silva, J.M.H.: J. High Energy Phys. 1104, 110 (2011) ADSCrossRefGoogle Scholar
  37. 37.
    da Rocha, R., Hoff da Silva, J.M.: Int. J. Geom. Methods Mod. Phys. 6, 461 (2009) MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    Bernardini, A.E., da Rocha, R.: arXiv:1203.1049 [hep-th] (2012)
  39. 39.
    Gillard, A., Martin, B.: arXiv:1012.5352 [hep-th] (2012)
  40. 40.
    Gillard, A.: arXiv:1109.4278 [hep-th] (2011)
  41. 41.
    Wunderle, K.E., Dick, R.: arXiv:1010.0963 [hep-th] (2010)
  42. 42.
    Lee, C.-Y.: arXiv:1011.5519 [hep-th] (2010)
  43. 43.
    Wei, H.: Phys. Lett. B 695, 307 (2011) ADSCrossRefGoogle Scholar
  44. 44.
    Basak, A., Bhatt, J.R.: J. Cosmol. Astropart. Phys. 1106, 011 (2011) ADSCrossRefGoogle Scholar
  45. 45.
    Liu, Y.X., Zhou, X.N., Yang, K., Chen, F.W.: arXiv:1107.2506 [hep-th] (2011)
  46. 46.
    Sadjadi, H.M.: arXiv:1109.1961 [gr-qc] (2011)
  47. 47.
    Fabbri, L.: Mod. Phys. Lett. A 25, 151 (2010) MathSciNetADSMATHCrossRefGoogle Scholar
  48. 48.
    Fabbri, L.: Mod. Phys. Lett. A 25, 2483 (2010) MathSciNetADSMATHCrossRefGoogle Scholar
  49. 49.
    Fabbri, L.: Gen. Relativ. Gravit. 43, 1607 (2011) MathSciNetADSMATHCrossRefGoogle Scholar
  50. 50.
    Fabbri, L.: Phys. Lett. B 704, 255 (2011) ADSCrossRefGoogle Scholar
  51. 51.
    Fabbri, L., Vignolo, S.: Ann. Phys. 524, 77 (2012) MathSciNetMATHCrossRefGoogle Scholar
  52. 52.
    Fabbri, L.: Phys. Rev. D 85, 047502 (2012) ADSCrossRefGoogle Scholar
  53. 53.
    Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972) Google Scholar
  54. 54.
    Misner, C., Thorne, K., Wheeler, J.A.: Gravitation. Freeman, New York (1973) Google Scholar
  55. 55.
    Macias, A., Lämmerzahl, C.: J. Math. Phys. 34, 4540 (1993) MathSciNetADSMATHCrossRefGoogle Scholar
  56. 56.
    Yu, X.: Astrophys. Space Sci. 154, 321 (1989) MathSciNetADSCrossRefGoogle Scholar
  57. 57.
    Socolovsky, M.: Ann. Fond. Louis Broglie 37 (2012) (to appear) Google Scholar
  58. 58.
    Fabbri, L.: Ann. Fond. Louis Broglie. Special Issue on Torsion (2007) Google Scholar
  59. 59.
    Fabbri, L.: Contemporary Fundamental Physics: Einstein and Hilbert. Nova Science, New York (2011) Google Scholar
  60. 60.
    Fabbri, L.: Ann. Fond. Louis Broglie 33, 365 (2008) MathSciNetGoogle Scholar
  61. 61.
    Fabbri, L.: Int. J. Theor. Phys. 51, 954 (2012) MathSciNetMATHCrossRefGoogle Scholar
  62. 62.
    Fabbri, L.: Mod. Phys. Lett. A (2012) Google Scholar
  63. 63.
    Fabbri, L.: arXiv:1108.3046 [gr-qc] (2011)
  64. 64.
    Fabbri, L.: Mod. Phys. Lett. A 26, 2091 (2011) ADSCrossRefGoogle Scholar
  65. 65.
    Fabbri, L.: Int. J. Theor. Phys. 50, 3616 (2011) MATHCrossRefGoogle Scholar
  66. 66.
    Fabbri, L.: Mod. Phys. Lett. A 26, 1697 (2011) ADSCrossRefGoogle Scholar
  67. 67.
    Fabbri, L.: arXiv:1009.4423 [hep-th] (2010)
  68. 68.
    Fabbri, L.: Ann. Fond. Louis Broglie 37 (2012) (to appear) Google Scholar
  69. 69.
    Fabbri, L., Vignolo, S.: Class. Quantum Gravity 28, 125002 (2011) MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.DIME Sez. Metodi e Modelli MatematiciUniversità di GenovaGenovaItaly
  2. 2.INFN & Dipartimento di FisicaUniversità di BolognaBolognaItaly

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