Transit cosmological models with perfect fluid and heat flow in Sáez-Ballester theory of gravitation

  • Umesh Kumar Sharma
  • Rashid ZiaEmail author
  • Anirudh Pradhan


In this paper, the Bianchi-V universe has been applied to the transitional universe. Exact solutions of Einstein’s modified field equations in the framework of Sáez-Ballester theory are obtained with heat conduction and perfect fluid. We have applied the hybrid expansion law for the average scale factor \(a = k t^{\alpha }e^{\beta t}\), (where \(\alpha \ge 0\), \(k > 0\), and \(\beta \ge 0\) are constants). This results into a new class of transit models from decelerating universe to the current accelerating universe. The present work also elucidates some of the physical, geometric and kinematic properties of the universe and found them in good agreement with recent observations.


Sáez-Ballester theory Bianchi type-V space-time Exact solutions Transit universe 



The authors sincerely acknowledge the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India, for providing facility where part of this work was completed during a visit. The authors also thank the editor and the anonymous referee for valuable comments which have improved the paper in present form.


  1. Akarsu O., Kumar S., Myrzakulov R., Sami M., Xu L. 2014, JCAP, 01, 022ADSCrossRefGoogle Scholar
  2. Amendola L. 2003, Mon. Not. Royal Astron. Soc., 342, 221ADSCrossRefGoogle Scholar
  3. Aubourg E., et al. 2015, Phys. Rev. D, 92, 123516ADSCrossRefGoogle Scholar
  4. Bamba K., Capozziello S., Nojiri S., Odintsov S. D. 2012, Astrophys. Space Sci., 342, 155ADSCrossRefGoogle Scholar
  5. Barber G. A. 1985, Gen. Rel. Gravit., 14, 117ADSCrossRefGoogle Scholar
  6. Bennett C. L., et al. 2003, Astrophys. J. Suppl., 148, 1ADSCrossRefGoogle Scholar
  7. Bernardis P. de., et al. 2000, Nature, 404, 955ADSCrossRefGoogle Scholar
  8. Brans C. H., Dicke R. H. 1961, Phys. Rev. A Ser-2, 124, 925Google Scholar
  9. Caldwell R. R., Komp W., Parker L., Vanzella D. A. T. 2006, Phys. Rev. D, 73, 023513ADSCrossRefGoogle Scholar
  10. Campanelli L., Cea P., Tedesco L. 2007, Phys. Rev. D, 76, 063007ADSCrossRefGoogle Scholar
  11. Capozziello S., Nojiri S., Odintsov S. D. 2006, Phys. Lett. B, 632, 597, [arXiv:hep-th/0507182]ADSCrossRefGoogle Scholar
  12. Clark D. H., Caswell J. L. 1976, MNRAS, 174, 267ADSCrossRefGoogle Scholar
  13. Clocchiatti A., et al. 2006, Astrophys. J., 642, 1ADSCrossRefGoogle Scholar
  14. Collins C. B. 1977, Jour. Math. Phys., 18, 2116ADSCrossRefGoogle Scholar
  15. Daile La, Steinhardt P. J. 1989, Phys. Rev. Lett., 62, 376 Erratum Phys. Rev. Lett. 62, (1989) 1066Google Scholar
  16. Dickey, J. M., Salpeter, E. E., Terzian, Y. 1978, Astrophys. J. Suppl. Ser., 36, 77ADSCrossRefGoogle Scholar
  17. Dunkley J., et al. 2009, Astrophys. J., 701, 1804ADSCrossRefGoogle Scholar
  18. Dunn K. A. 1974, J. Math. Phys., 15, 2229ADSCrossRefGoogle Scholar
  19. Elizalde E., Nojiri S., Odintsov S. D. 2004, Phys. Rev. D, 70, 043539, [arXiv:hep-th/0405034]ADSCrossRefGoogle Scholar
  20. Esmaeili F. M., Mishra B. 2018, J. Asrtophys. Astr., 39, 59ADSCrossRefGoogle Scholar
  21. Hanany S., et al. 2000, Astrophys. J. Lett., 545, L5ADSCrossRefGoogle Scholar
  22. Hinshaw G., et al. 2009, Astrophys. J. Suppl., 180, 225, [arXiv:0803.0732].
  23. Hinshaw G., et al. 2007, Astrophys. J. Suppl., 170, 288ADSCrossRefGoogle Scholar
  24. Hoftuft J., et al. 2009, Astrophys. J., 699, 985ADSCrossRefGoogle Scholar
  25. Jaffe J., et al. 2006, Astrophys. J., 643, 616ADSCrossRefGoogle Scholar
  26. Jaiswal R., Zia R. 2018, Indian J. Phys., 92, 1075ADSCrossRefGoogle Scholar
  27. Jamil M., Ali S., Momeni D., Myrzakulov R. 2012, Eur. Phys. J. C, 72, 1998ADSCrossRefGoogle Scholar
  28. Katore S. D., Adhav K. S., Shaikh A. Y., Sarkate N. K. 2010, Int. J. Theor. Phys., 49, 2358Google Scholar
  29. Koivisto T., Mota D. F. 2018, J. Cosmol. Astropart. Phys., 06, 018ADSGoogle Scholar
  30. Koivisto T., Mota D. F. 2008, J. Cosmol. Astropart. Phys., 08, 021ADSCrossRefGoogle Scholar
  31. Kumar S. 2013, Grav. & Cosmol., 19, 284ADSCrossRefGoogle Scholar
  32. MacCallum M. A. H. 1971, Commun. Math. Phys., 20, 57ADSCrossRefGoogle Scholar
  33. Mahanta C. R., Sharma N. 2017, New Astronomy, 57, 70ADSCrossRefGoogle Scholar
  34. Misner C. W. 1968, Astrophys. J., 151, 431ADSCrossRefGoogle Scholar
  35. Nojiri S., Odintsov S. D. 2004, Gen. Rel. Grav., 38, 1285ADSCrossRefGoogle Scholar
  36. Nordtvedt K. 1970, Astrophys. J., 161, 1059ADSMathSciNetCrossRefGoogle Scholar
  37. Padmanabhan T., Roychowdhury T. 2003, Mon. Not. R. Astron. Soc., 344, 823ADSCrossRefGoogle Scholar
  38. Perlmutter S., et al. 1999, Astrophys. J., 517, 565ADSCrossRefGoogle Scholar
  39. Piemental L. O. 1997, Mod. Phys. Lett. A, 12, 1865ADSCrossRefGoogle Scholar
  40. Pradhan A., Singh A. K., Chouhan D. S. 2013, Int. J. Theor. Phys., 52, 266CrossRefGoogle Scholar
  41. Pradhan A., Amirhashchi H. 2011, Mod. Phys. Lett. A, 26, 2261ADSCrossRefGoogle Scholar
  42. Pradhan A., Saha S., Rikhvitsky V. 2015, Indian J. Phys., 89, 503ADSCrossRefGoogle Scholar
  43. Radhakrishnan, G. C. et al. 1980, in Evans A., Bode M. F., eds, Non-Solar Gamma Rays (COSPAR), Pergamon Press, Oxford, p. 163Google Scholar
  44. Ram S., Zeyauddin M., Singh C. P. 2009, Pramana J. Phys., 72, 415ADSCrossRefGoogle Scholar
  45. Rao V. U. M., Divya U. Y., Prasanthi 2017, Eur. Phys. J. Plus, 132, 64Google Scholar
  46. Reddy D. R. K., Naidu R. L., Rao V. U. M. 2006, Astrophys. Space Sci., 306, 185ADSCrossRefGoogle Scholar
  47. Riess A. G., et al. 2011, Astrophys. J., 730, 119, Erratum-Ibid 732, 129Google Scholar
  48. Riess A. G., et al. 2004, Astrophys. J., 607, 665ADSCrossRefGoogle Scholar
  49. Riess A. G., et al. 2001, Astrophys. J., 560, 49ADSCrossRefGoogle Scholar
  50. Riess A. G., et al. 1998, Astron. J., 116, 1009ADSCrossRefGoogle Scholar
  51. Ross D. K. 1972, Phys. Rev. D, 5, 284ADSCrossRefGoogle Scholar
  52. Sáez D., Ballester V. J. 1986, Phys. Lett. A, 113, 467ADSCrossRefGoogle Scholar
  53. Santos M. V. dos., Reis R. R., Waga I. 2016, JCAP, 02, 066, arXiv:1505.0381.
  54. Starrfield S., Iliadis C., Hix W. R. 2008, in Bode M. F., Evans A., eds, Classical Novae, 2nd edition, Cambridge University Press, Cambridge, p. 77CrossRefGoogle Scholar
  55. Tonry J. L., et al. 2003, Astrophys. J., 594, 1ADSCrossRefGoogle Scholar
  56. Van Loon J. T. 2008, in Evans A. et al., eds, R S Ophiuchi (2006) and the Recurrent Nova Phenomenon, ASP Conference Series, Volume 401, p. 90Google Scholar
  57. Wagoner R. V. 1970, Phys. Rev. D, 1, 3209ADSCrossRefGoogle Scholar
  58. Yadav A. K., Srivastava P. K., Yadav L. 2015, Int. J. Theor. Phys., 54, 1671CrossRefGoogle Scholar
  59. Zwicky, F. 1957, Morphological Astronomy, Springer-Verlag, Berlin, p. 258CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  • Umesh Kumar Sharma
    • 1
  • Rashid Zia
    • 1
    Email author
  • Anirudh Pradhan
    • 1
  1. 1.Department of MathematicsGLA UniversityMathuraIndia

Personalised recommendations