Skip to main content
SpringerLink
Log in

LRS Bianchi Type II Perfect Fluid Cosmological Models in Normal Gauge for Lyra’s Manifold

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The present study deals with spatially homogeneous and locally rotationally symmetric (LRS) Bianchi type II cosmological models of perfect fluid distribution of matter for the field equations in normal gauge for Lyra’s manifold where gauge function β is taken as time dependent. To get the deterministic models of the universe, we assume that the expansion (θ) in the model is proportional to the shear (σ). This leads to condition R=mS n, where R and S are metric potentials, m and n are constants. We have obtained two types of models of the universe for two different values of n. It has been found that the displacement vector β behaves like cosmological term Λ in the normal gauge treatment and the solutions are consistent with recent observations. Some physical and geometric behavior of these models are also discussed.

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. Lyra, G.: Math. Z. 54, 52 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  2. Sen, D.K.: Z. Phys. 149, 311 (1957)

    Article  MATH  ADS  Google Scholar 

  3. Sen, D.K., Dunn, K.A.: J. Math. Phys. 12, 578 (1971)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. Halford, W.D.: Aust. J. Phys. 23, 863 (1970)

    ADS  Google Scholar 

  5. Halford, W.D.: J. Math. Phys. 13, 1699 (1972)

    Article  ADS  Google Scholar 

  6. Sen, D.K., Vanstone, J.R.: J. Math. Phys. 13, 990 (1972)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Soleng, H.H.: Gen. Relativ Gravit. 19, 1213 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  8. Singh, T., Singh, G.P.: J. Math. Phys. 32, 2456 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Singh, T., Singh, G.P.: Nuovo Cimento B 106, 617 (1991)

    Article  ADS  Google Scholar 

  10. Singh, T., Singh, G.P.: Int. J. Theor. Phys. 31, 1433 (1992)

    Article  Google Scholar 

  11. Singh, T., Singh, G.P.: Fortschr. Phys. 41, 737 (1993)

    MathSciNet  Google Scholar 

  12. Singh, G.P., Desikan, K.: Pramana J. Phys. 49, 205 (1997)

    Article  ADS  Google Scholar 

  13. Pradhan, A., Vishwakarma, A.K.: J. Geom. Phys. 49, 332 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. Pradhan, A., Yadav, V.K., Chakrabarty, I.: Int. J. Mod. Phys. D 10, 339 (2000)

    Article  ADS  Google Scholar 

  15. Pradhan, A., Yadav, L., Yadav, A.K.: Astrophys. Space Sci. 299, 31 (2005)

    Article  ADS  Google Scholar 

  16. Rahaman, F., Chakraborty, S., Kalam, M.: Int. J. Mod. Phys. D 10, 735 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. Bhowmik, B.B., Rajput, A.: Pramana J. Phys. 62, 1187 (2004)

    Article  ADS  Google Scholar 

  18. Matyjasek, J.: Int. J. Theor. Phys. 33, 967 (1994) 967

    Article  MATH  MathSciNet  Google Scholar 

  19. Reddy, D.R.K.: Astrophys. Space Sci. 300, 381 (2005)

    Article  ADS  Google Scholar 

  20. Casama, R., de Melo, C.A.M., Pimentel, B.M.: Astrophys. Space Sci. 305, 125 (2006)

    Article  ADS  Google Scholar 

  21. Rahaman, F., Ghosh, P.: Fizika B 13, 719 (2004)

    ADS  Google Scholar 

  22. Rahaman, F., Bhui, B., Bag, G.: Astrophys. Space Sci. 295, 507 (2005)

    Article  ADS  Google Scholar 

  23. Rahaman, F.: Int. J. Mod. Phys. D 9, 775 (2000) 775

    MATH  MathSciNet  ADS  Google Scholar 

  24. Rahaman, F.: Int. J. Mod. Phys. D 10, 579 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  25. Rahaman, F.: Astrophys. Space Sci. 281, 595 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  26. Shanthi, K., Rao, V.U.M.: Astrophys. Space Sci. 179, 147 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  27. Venkateswarlu, R., Reddy, D.R.K.: Astrophys. Space Sci. 182, 97 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

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

    MATH  ADS  Google Scholar 

  29. Hoyle, F., Narlikar, J.V.: Proc. R. Soc. Lond. Ser. A 277, 1 (1964)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. Hoyle, F., Narlikar, J.V.: Proc. R. Soc. Lond. Ser. A 278, 465 (1964)

    Article  MATH  ADS  Google Scholar 

  31. Pradhan, A., Aotemshi, I., Singh, G.P.: Astrophys. Space Sci. 288, 315 (2003)

    Article  MATH  ADS  Google Scholar 

  32. Pradhan, A., Rai, V., Otarod, S.: Fizika B 15, 23 (2006)

    Google Scholar 

  33. Pradhan, A., Rai, K.K., Yadav, A.K.: Braz. J. Phys. 37, 1084 (2007)

    Article  Google Scholar 

  34. Pradhan, A.: J. Math. Phys. 50, 022501 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  35. Pradhan, A., Kumhar, S.S.: Astrophys. Space Sci. 321, 137 (2009)

    Article  ADS  Google Scholar 

  36. Pradhan, A., Mathur, P.: Fizika B 18, 243 (2009)

    Google Scholar 

  37. Pradhan, A., Ram, P.: Int. J. Theor. Phys. 48, 3188 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  38. Casama, R., Melo, C., Pimentel, B.: Astrophys. Space Sci. 305, 125 (2006)

    Article  ADS  Google Scholar 

  39. Bali, R., Chandnani, N.K.: J. Math. Phys. 49, 032502 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  40. Bali, R., Chandnani, N.K.: Fizika B 18, 227 (2009)

    Google Scholar 

  41. Kumar, S., Singh, C.P.: Int. Mod. Phys. A 23, 813 (2008)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  42. Ram, S., Zeyauddin, M., Singh, C.P.: Int. J. Mod. Phys. A 23, 4991 (2008)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  43. Singh, J.K.: Astrophys. Space Sci. 314, 361 (2008)

    Article  ADS  Google Scholar 

  44. Rao, V.U.M., Vinutha, T., Santhi, M.V.: Astrophys. Space Sci. 314, 213 (2008)

    Article  ADS  Google Scholar 

  45. Thorne, K.S.: Astrophys. J. 148, 51 (1967)

    Article  ADS  Google Scholar 

  46. Kantowski, R., Sachs, R.K.: J. Math. Phys. 7, 433 (1966)

    Article  MathSciNet  ADS  Google Scholar 

  47. Kristian, J., Sachs, R.K.: Astrophys. J. 143, 379 (1966)

    Article  MathSciNet  ADS  Google Scholar 

  48. Collins, C.B., Glass, E.N., Wilkinson, D.A.: Gen. Relativ. Gravit. 12, 805 (1980)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  49. Bali, R., Banerjee, R.: J. Rajasthan Acad. Phys. Sci. 7, 55 (2008)

    MATH  Google Scholar 

  50. Perlmutter, S., et al.: Astrophys. J. 483, 565 (1997)

    Article  ADS  Google Scholar 

  51. Perlmutter, S., et al.: Nature 391, 51 (1998)

    Article  ADS  Google Scholar 

  52. Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  53. Reiss, A.G., et al.: Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  54. Reiss, A.G., et al.: Astron. J. 607, 665 (2004)

    Google Scholar 

  55. MacCallum, M.A.H.: Commput. Math. Phys. 20, 57 (1971)

    Article  MathSciNet  ADS  Google Scholar 

  56. Gunn, J., Tinsley, B.M.: Nature 257, 454 (1975)

    Article  ADS  Google Scholar 

  57. Wampler, E.J., Burke, W.L.: In: Bertola, F., Sulentix, J.W., Madora, B.F. (eds.) New Ideas in Astronomy, p. 317. Cambridge University Press, Cambridge (1988)

    Google Scholar 

  58. Sakharov, A.D.: Dokl. Akad. Nauk SSSR 177, 70 (1968) [translation, Sov. Phys. Dokl. 12, 1040 (1968)]

    ADS  Google Scholar 

  59. Peeble, P.J.E., Ratra, B.: Astrophys. J. 325, L17 (1988)

    Article  ADS  Google Scholar 

  60. Ellis, G.F.R.: Standard and Inflationary Cosmologies, Preprint SISSA, Trieste, 176/90/A (1990)

  61. La, D., Steinhardt, P.J.: Phys. Rev. Lett. 62, 376 (1989)

    Article  ADS  Google Scholar 

  62. Barrow, J.D.: Phys. Lett. B 235, 40 (1990)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Uttaranchal Institute of Technology, Arcadia Grant, Chandanwari, Dehradun, 248 007, India

    Shilpi Agarwal

  2. Department of Mathematics, D.B.S. Post-graduate College, Dehradun, 248 001, India

    R. K. Pandey

  3. Department of Mathematics, Hindu Post-graduate College, Zamania, 232 331, Ghazipur, India

    Anirudh Pradhan

Authors
  1. Shilpi Agarwal
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. K. Pandey
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anirudh Pradhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anirudh Pradhan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Agarwal, S., Pandey, R.K. & Pradhan, A. LRS Bianchi Type II Perfect Fluid Cosmological Models in Normal Gauge for Lyra’s Manifold. Int J Theor Phys 50, 296–307 (2011). https://doi.org/10.1007/s10773-010-0523-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-010-0523-y

Keywords

Search

Navigation