Advertisement

International Journal of Theoretical Physics

, Volume 52, Issue 3, pp 735–749 | Cite as

A New Class of Bianchi Cosmological Models in Lyra’s Geometry

  • R. Chaubey
  • A. K. Shukla
Article

Abstract

The new class of cosmological model of the early Universe filled with perfect fluid in Lyra’s geometry has been considered. We obtain two classes of exact solutions of the field equations in Lyra’s geometry with a time-dependent displacement vector. The exact solutions to the corresponding field equations are obtained in quadrature form. The cosmological parameters have been discussed in detail and it is also shown that the solutions tend asymptotically to isotropic Friedmann-Robertson-Walker cosmological model. We have also discussed the well-known astrophysical phenomena, namely the Hubble parameter H(z), luminosity distance d L and distance modulus μ(z) with redshift.

Keywords

Cosmological Model Deceleration Parameter Luminosity Distance Average Scale Factor Constant Deceleration Parameter 
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.

References

  1. 1.
    Weyl, H.: Math. Z. 54, 52 (1951) MathSciNetCrossRefGoogle Scholar
  2. 2.
    Lyra, G.: Z. Phys. 149, 311 (1951) Google Scholar
  3. 3.
    Singh, T., Singh, G.P.: J. Math. Phys. 32, 2456 (1991) MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    Singh, T., Singh, G.P.: Fortschr. Phys. 41, 737 (1993) MathSciNetGoogle Scholar
  5. 5.
    Sen, D.K., Dunn, K.A.: J. Math. Phys. 12, 578 (1971) MathSciNetADSzbMATHCrossRefGoogle Scholar
  6. 6.
    Halford, W.D.: J. Math. Phys. 13, 1399 (1972) CrossRefGoogle Scholar
  7. 7.
    Bhamara, K.S.: Aust. J. Phys. 27, 541 (1974) ADSCrossRefGoogle Scholar
  8. 8.
    Karade, T.M., Borikar, S.M.: Gen. Relativ. Gravit. 9, 431 (1978) MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    Reddy, D.R.K., Innaiah, P.: Astrophys. Space Sci. 136, 191 (1987) ADSCrossRefGoogle Scholar
  10. 10.
    Soleng, H.H.: Gen. Relativ. Gravit. 19, 1213 (1987) MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    Hoyle, F.: Mon. Not. R. Astron. Soc. 108, 252 (1948) ADSGoogle Scholar
  12. 12.
    Hoyle, F., Narlikar, J.V.: Pro. R. Soc. Lond. Ser. A 273, 1 (1963) MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. 13.
    Hoyle, F., Narlikar, J.V.: Pro. R. Soc. Lond. Ser. A 282, 178 (1964) MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Beesham, A.: Aust. J. Phys. 41, 833 (1988) MathSciNetADSGoogle Scholar
  15. 15.
    Singh, T., Singh, G.P.: Nuovo Cimento B 106, 617 (1991) ADSCrossRefGoogle Scholar
  16. 16.
    Singh, T., Singh, G.P.: Int. J. Theor. Phys. 31, 1433 (1992) CrossRefGoogle Scholar
  17. 17.
    Singh, G.P., Desikan, K.: Pramana J. Phys. 49, 205 (1997) ADSCrossRefGoogle Scholar
  18. 18.
    Ram, S., Singh, P.: Int. J. Theor. Phys. 31, 2095 (1992) MathSciNetCrossRefGoogle Scholar
  19. 19.
    Singh, C.P.: Astrophys. Space Sci. 275, 377 (2003) ADSCrossRefGoogle Scholar
  20. 20.
    Pradhan, A., Vishwakarma, A.K.: J. Geom. Phys. 49, 332 (2004) MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. 21.
    Rahaman, F., Begum, N., Bag, G., Bhui, B.C.: Astrophys. Space Sci. 299, 211 (2005) ADSCrossRefGoogle Scholar
  22. 22.
    Kumar, S., Singh, C.P.: Int. J. Mod. Phys. A 23, 813 (2008) MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. 23.
    Singh, G.P., Kale, A.Y.: Int. J. Theor. Phys. 48, 2095 (2009) Google Scholar
  24. 24.
    Ram, S., Zeyauddin, M., Singh, C.P.: J. Geom. Phys. 60, 3049 (2010) MathSciNetCrossRefGoogle Scholar
  25. 25.
    Chaubey, R.: Int. J. Theor. Phys. (2012). doi: 10.1007/s10773-012-1285-5 Google Scholar
  26. 26.
    Coley, A.A.: Dynamical Systems and Cosmology. Kluwer Academic, Dordrecht (2003) zbMATHGoogle Scholar
  27. 27.
    Nilsson, U.S., Uggla, C., Wainwright, J., Lim, W.C.: Appl. J. Lett. 522, L1 (1999) ADSCrossRefGoogle Scholar
  28. 28.
    Sen, D.K.: Z. Phys. 149, 311 (1971) ADSGoogle Scholar
  29. 29.
    Akarsu, O., Dereli, T.: Int. J. Theor. Phys. 51, 612 (2012) zbMATHCrossRefGoogle Scholar
  30. 30.
    Collins, C.B., Hawking, S.W.: Astrophys. J. 180, 317 (1973) MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    Chiba, T., Nakamura, T.: Prog. Theor. Phys. 100, 1077 (1998) ADSCrossRefGoogle Scholar
  32. 32.
    Sahni, V.: arXiv:astro-ph/0211084 (2002)
  33. 33.
    Blandford, R.D., Amin, M., Baltz, E.A., Mandel, K., Marshall, P.L.: arXiv:astro-ph/0408279 (2004)
  34. 34.
    Visser, M.: Class. Quantum Gravity 21, 2603 (2004) MathSciNetADSzbMATHCrossRefGoogle Scholar
  35. 35.
    Visser, M.: Gen. Relativ. Gravit. 37, 1541 (2005) MathSciNetADSzbMATHCrossRefGoogle Scholar
  36. 36.
    Riess, A.G., et al. (Supernova Search Team): Astrophys. J. 607, 665 (2004) ADSCrossRefGoogle Scholar
  37. 37.
    Astier, P., et al. (SNLS): Astron. Astrophys. 447, 31 (2006) ADSCrossRefGoogle Scholar
  38. 38.
    Rapetti, D., Allen, S.W., Amin, M.A., Blandford, R.D.: Mon. Not. R. Astron. Soc. 375, 1510 (2007) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.DST-Centre for Interdisciplinary Mathematical Sciences, Faculty of ScienceBanaras Hindu UniversityVaranasiIndia

Personalised recommendations