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Bianchi type-VIII spinor solutions

  • Bijan Saha
Regular Article

Abstract.

Within the scope of Bianchi type-VIII space-time the role of nonlinear spinor field in the evolution of the Universe is studied. It is found that, unlike the diagonal Bianchi models, in this case the components of energy-momentum tensor of spinor field along the principal axis are not the same, i.e. \(T_{1}^{1} \ne T_{2}^{2} \ne T_{3}^{3}\), even in the absence of spinor field nonlinearity. The presence of nontrivial non-diagonal components of energy-momentum tensor of the spinor field imposes severe restrictions both on geometry of space-time and on the spinor field itself. While the energy-momentum with diagonal components alone allows only locally rotational symmetry, say \(a_{1} \sim a_{2}\), in this case there might be a second case with \(a_{1} \sim a_{2} \sim a_{3}\) . It was found that, like a Bianchi type-IX case, a positive \(\lambda_{1}\) gives rise to an oscillatory mode of expansion, while a trivial \(\lambda_{1}\) leads to rapid expansion at the early stage of evolution.

References

  1. 1.
    V.A. Belinskii, I.M. Khalatnikov, E.M. Lifshitz, Adv. Phys. 19, 525 (1970)ADSCrossRefGoogle Scholar
  2. 2.
    C.B. Collins, S.W. Hawking, Astrophys. J. 180, 317 (1973)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    J.D. Barrow, Y. Gasper, Class. Quantum Grav. 18, 1809 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    Hans Ringström, Class. Quantum Grav. 17, 713 (2000)CrossRefGoogle Scholar
  5. 5.
    Hans Ringström, Class. Quantum Grav. 18, 3791 (2001)CrossRefGoogle Scholar
  6. 6.
    Hans Ringström, Class. Quantum Grav. 20, 1943 (2003)CrossRefGoogle Scholar
  7. 7.
    S. Hervik, W.C. Lim, Class. Quantum Grav. 23, 3017 (2006)CrossRefGoogle Scholar
  8. 8.
    B. Saha, G.N. Shikin, Gen. Relativ. Gravit. 29, 1099 (1997)ADSCrossRefGoogle Scholar
  9. 9.
    B. Saha, G.N. Shikin, J. Math. Phys. 38, 5305 (1997)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    B. Saha, Phys. Rev. D 64, 123501 (2001)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    B. Saha, Phys. Rev. D 69, 124006 (2004)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    B. Saha, T. Boyadjiev, Phys. Rev. D 69, 124010 (2004)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    N.J. Popławski, Phys. Lett. B 690, 77 (2010)Google Scholar
  14. 14.
    N.J. Popławski, Phys. Rev. D 85, 107502 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    N.J. Popławski, Gen. Relativ. Gravit. 44, 1007 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    L. Fabbri, A Int. J. Theor. Phys. 52, 634 (2013)CrossRefGoogle Scholar
  17. 17.
    B. Saha, Phys. Part. Nucl. 37, S13 (2006)CrossRefGoogle Scholar
  18. 18.
    M.O. Ribas, F.P. Devecchi, G.M. Kremer, Phys. Rev. D 72, 123502 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    B. Saha, Phys. Rev. D 74, 124030 (2006)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    B. Saha, Gravit. Cosmol. 12, 215 (2006)ADSGoogle Scholar
  21. 21.
    B. Saha, Roman. Rep. Phys. 59, 649 (2007)Google Scholar
  22. 22.
    B. Saha, Phys. Part. Nucl. 40, 656 (2009)CrossRefGoogle Scholar
  23. 23.
    L. Fabbri, Phys. Rev. D 85, 047502 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    L. Fabbri, Gen. Relativ. Gravit. 43, 1607 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    V.G. Krechet, M.L. Fil’chenkov, G.N. Shikin, Gravit. Cosmol. 14, 292 (2008)ADSMathSciNetCrossRefGoogle Scholar
  26. 26.
    B. Saha, Cent. Eur. J. Phys. 8, 920 (2010)Google Scholar
  27. 27.
    B. Saha, Roman. Rep. Phys. 62, 209 (2010)Google Scholar
  28. 28.
    B. Saha, Astrophys. Space Sci. 331, 243 (2011)ADSCrossRefGoogle Scholar
  29. 29.
    B. Saha, Int. J. Theor. Phys. 51, 1812 (2012)CrossRefGoogle Scholar
  30. 30.
    B. Saha, Canadian J. Phys. 93, 1 (2015)ADSCrossRefGoogle Scholar
  31. 31.
    B. Saha, Chinese J. Phys. 53, 110114 (2015)Google Scholar
  32. 32.
    B. Saha, Int. J. Theor. Phys. 55, 2259 (2016)CrossRefGoogle Scholar
  33. 33.
    B. Saha, Eur. Phys. J. Plus. 131, 170 (2016)CrossRefGoogle Scholar
  34. 34.
    Bijan Saha, arXiv:1705.07773 [gr-qc]Google Scholar
  35. 35.
    Bijan Saha, Gravit. Cosmol. 19, 65 (2013)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Laboratory of Information TechnologiesJoint Institute for Nuclear ResearchMoscow regionRussia

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