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Anisotropic Viscous Fluid Cosmological Models from Deceleration to Acceleration in String Cosmology

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Abstract

In the present study, anisotropic locally rotationally symmetric (LRS) Bianchi type II models representing massive strings have been presented with variable mean deceleration parameter. The field equations in scalar-tensor theory with energy momentum tensor proposed by Letelier (Phys. Rev. D 28: 2414, 1983), have been solved for the bulk viscous fluid and perfect fluid under the following physically relevant assumptions: (a) scale factor varies with time as \(a(t) = (\sinh(\alpha t))^{\frac{1}{n}}\), (b) Expansion (θ) in the model is proportional to shear (σ), (c) p=γρ, where γ (0≤γ≤1) is a constant, (d) ξ(t)=ξ 0 ρ η. It has been observed that the presented universe has a phase transition from the early decelerating phase to the accelerating phase at present epoch which is in good agreement with the recent astronomical observations. Moreover, some physical and geometric properties of the models have been discussed in detail.

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References

  1. Kumar, S., Akarsu, Ö.: Eur. Phys. J. Plus 127, 64 (2012)

    Article  Google Scholar 

  2. Campanelli, L., Cea, P., Tedesco, L.: Phys. Rev. Lett. 97, 131302 (2006)

    Article  ADS  Google Scholar 

  3. Campanelli, L., Cea, P., Tedesco, L.: Phys. Rev. D 76, 063007 (2007)

    Article  ADS  Google Scholar 

  4. Campanelli, L., Cea, P., Fogli, G.L., Tedesco, L.: Int. J. Mod. Phys. D 20, 1153 (2011)

    Article  ADS  MATH  Google Scholar 

  5. Campanelli, L., Cea, P., Fogli, G.L., Tedesco, L.: Mod. Phys. Lett. A 26, 1169 (2011)

    Article  ADS  Google Scholar 

  6. Brans, C., Dicke, R.H.: Phys. Rev. 124, 925 (1961)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. Barber, G.A.: Gen. Relativ. Gravit. 14, 117 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  8. Sáez, D., Ballester, V.J.: Phys. Lett. A 113, 467 (1986)

    Article  ADS  Google Scholar 

  9. Mathiazhagan, C., Johri, V.B.: Class. Quantum Gravity 1, L29 (1984)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Linde, A.: Phys. Lett. B 238, 160 (1990)

    Article  ADS  Google Scholar 

  12. Kibble, T.W.B.: J. Phys. A, Math. Gen. 9, 1387 (1976)

    Article  ADS  MATH  Google Scholar 

  13. Zel’dovich, Ya.B., Kobzarev, I.Yu., Okun, L.B.: Sov. Phys. JETP 40, 1 (1975)

    ADS  Google Scholar 

  14. Kibble, T.W.B.: Phys. Rep. 67, 183 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  15. Everett, A.E.: Phys. Rev. D 24, 858 (1981)

    Article  ADS  Google Scholar 

  16. Vilenkin, A.: Phys. Rev. D 24, 2082 (1981)

    Article  ADS  Google Scholar 

  17. Zel’dovich, Ya.B.: Mon. Not. R. Astron. Soc. 192, 663 (1980)

    ADS  Google Scholar 

  18. Letelier, P.S.: Phys. Rev. D 28, 2414 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  19. Stachel, J.: Phys. Rev. D 21, 2171 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  20. Roy, S.R., Banerjee, S.K.: Class. Quantum Gravity 12, 1943 (1995)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  21. Wang, X.X.: Astrophys. Space Sci. 293, 433 (2004)

    Article  ADS  Google Scholar 

  22. Jotania, K., Yadav, P., Faruqi, S.A.: Int. J. Theor. Phys. 50, 1424 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  23. Pradhan, A., Ram, P., Singh, R.: Astrophys. Space Sci. 331, 275 (2011)

    Article  ADS  Google Scholar 

  24. Pradhan, A., Amirhashchi, H., Yadav, M.K.: Fizika B 18, 35 (2009)

    Google Scholar 

  25. Pradhan, A., Chouhan, D.S.: Astrophys. Space Sci. 331, 697 (2011)

    Article  ADS  Google Scholar 

  26. Bali, R., Pradhan, A.: Chin. Phys. Lett. 24, 585 (2007)

    Article  Google Scholar 

  27. Saha, B., Visinescu, M.: Int. J. Theor. Phys. 49, 1411 (2010)

    Article  MATH  Google Scholar 

  28. Naidu, R.L., Satyanarayana, B., Reddy, D.R.K.: Astrophys. Space Sci. 338, 351 (2012)

    Article  ADS  MATH  Google Scholar 

  29. Misner, C.W.: Astrophys. J. 151, 431 (1968)

    Article  ADS  Google Scholar 

  30. Eckart, C.: Phys. Rev. 58, 919 (1940)

    Article  ADS  Google Scholar 

  31. Landau, L.D., Lifshitz, E.M.: Fluid Mechanics p. 47. Pergamon, New York (1959)

    Google Scholar 

  32. Grøn, Ø.: Astrophys. Space Sci. 173, 191 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  33. Singh, C.P., Kumar, S.: Astrophys. Space Sci. 323, 407 (2009)

    Article  ADS  Google Scholar 

  34. Kremer, G.M., Devecchi, F.P.: Phys. Rev. D 67, 047301 (2003)

    Article  ADS  Google Scholar 

  35. Debnath, P.S., Paul, B.C., Beesham, A.: Phys. Rev. D 76, 123505 (2007)

    Article  ADS  Google Scholar 

  36. Yadav, A.K.: Int. J. Theor. Phys. 50, 1664 (2011)

    Article  MATH  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  38. Singh, C.P., Kumar, S., Pradhan, A.: Class. Quantum Gravity 24, 455 (2007)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  39. Riess, A.G., et al.: Astron. J. 116, 1009 (1998)

    Article  ADS  Google Scholar 

  40. Riess, A.G., et al.: Astrophys. J. 607, 665 (2004)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Tonry, J.L., et al.: Astrophys. J. 594, 1 (2003)

    Article  ADS  Google Scholar 

  43. Clocchiatti, A., et al.: Astrophys. J. 642, 1 (2006)

    Article  ADS  Google Scholar 

  44. Bennett, C.L., et al.: Astrophys. J. Suppl. 148, 1 (2003)

    Article  ADS  Google Scholar 

  45. de Bernardis, P., et al.: Nature 404, 955 (2000)

    Article  ADS  Google Scholar 

  46. Hanany, S., et al.: Astrophys. J. 545, L5 (2000)

    Article  ADS  Google Scholar 

  47. Cunha, J.V., Lima, J.A.S.: Mon. Not. R. Astron. Soc. 390, 210 (2008)

    Article  ADS  Google Scholar 

  48. Cunha, J.V.: Phys. Rev. D 79, 047301 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  49. Frieman, J.A., Turner, M.S., Huterer, D.: Annu. Rev. Astron. Astrophys. 46, 385 (2008)

    Article  ADS  Google Scholar 

  50. Melchiorri, A., Pagano, L., Pandolfi, S.: Phys. Rev. D 76, 041301 (2007)

    Article  ADS  Google Scholar 

  51. Ishida, E.E.O., Reis, R.R.R., Toribio, A.V., Waga, I.: Astropart. Phys. 28, 547 (2007)

    Article  ADS  Google Scholar 

  52. Pandolfi, S.: Nucl. Phys. B 194, 294 (2009)

    Article  Google Scholar 

  53. Lima, J.A.S., Holanda, R.F.L., Cunha, J.V.: AIP Conf. Proc. 1241, 224 (2009)

    ADS  Google Scholar 

  54. Riess, A.G., et al.: Astrophys. J. 659, 98 (2007)

    Article  ADS  Google Scholar 

  55. Astier, P., et al.: Astron. Astrophys. 447, 31 (2006)

    Article  ADS  Google Scholar 

  56. Davis, T.M., et al.: Astrophys. J. 666, 716 (2007)

    Article  ADS  Google Scholar 

  57. Lima, J.A.S., Jesus, J.F., Santos, R.C., Gill, M.S.S.: (2012). arXiv:1205.4688v2 [astro-ph.CO]

  58. Li, Z., Wu, P., Yu, H.: Phys. Lett. B 695, 1 (2011)

    Article  ADS  Google Scholar 

  59. Saha, B., Yadav, A.K.: Astrophys. Space Sci. 341, 651 (2012)

    Article  ADS  Google Scholar 

  60. Pradhan, A., Jaiswal, R., Jotania, K., Khare, R.K.: Astrophys. Space Sci. 337, 401 (2012)

    Article  ADS  MATH  Google Scholar 

  61. Amirhashchi, H., Pradhan, A., Saha, B.: Chin. Phys. Lett. 28, 039801 (2011)

    Article  Google Scholar 

  62. Akarsu, Ö., Dereli, T.: Int. J. Theor. Phys. 51, 612 (2012)

    Article  MATH  Google Scholar 

  63. Chawla, C., Mishra, R.K., Pradhan, A.: (2012). arXiv:1203.4014 [physics.gen-ph]

  64. Chawla, C., Mishra, R.K.: Rom. J. Phys. 58(1–2) (2013, to appear)

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

    Article  ADS  Google Scholar 

  66. Kantowski, R., Sachs, R.K.: J. Math. Phys. 7, 443 (1966)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  68. Pradhan, A., Amirhashchi, H., Jaiswal, R.: Astrophys. Space Sci. 334, 249 (2011)

    Article  ADS  Google Scholar 

  69. Zel’dovich, Ya.B.: Sov. Phys. JETP 14, 1143 (1962)

    MATH  Google Scholar 

  70. Pavon, D., Bafaluy, J., Jou, D.: Class. Quantum Gravity 8, 347 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  71. Maartens, R.: Class. Quantum Gravity 12, 1455 (1995)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  72. Santos, N.O., Dias, R.S., Banerjee, A.: J. Math. Phys. 26, 878 (1985)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  73. Murphy, G.L.: Phys. Rev. D 8, 4231 (1973)

    Article  ADS  Google Scholar 

  74. Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972)

    Google Scholar 

  75. Belinskii, V.A., Khalatnikov, I.M.: Sov. Phys. JETP 42, 205 (1976)

    ADS  Google Scholar 

  76. MacCallum, M.A.H.: Commun. Math. Phys. 20, 57 (1971)

    Article  ADS  MathSciNet  Google Scholar 

  77. Verma, M.K., Singh, M.K., Ram, S.: Int. J. Theor. Phys. 51, 1729 (2012)

    Article  MATH  Google Scholar 

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Acknowledgements

The financial support as JRF (Sanction No. 09/797(0007)/2010-EMR-I) in part by CSIR, New Delhi, India is gratefully acknowledged by C. Chawla. The authors thank the anonymous referee whose valuable comments and suggestions have helped us to submit the revised version of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal, 148106, Punjab, India

    R. K. Mishra & Chanchal Chawla

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

    Anirudh Pradhan

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  1. R. K. Mishra
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Mishra, R.K., Pradhan, A. & Chawla, C. Anisotropic Viscous Fluid Cosmological Models from Deceleration to Acceleration in String Cosmology. Int J Theor Phys 52, 2546–2559 (2013). https://doi.org/10.1007/s10773-013-1540-4

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