Skip to main content
SpringerLink
Log in

Bianchi type \({\hbox {VI}}_0\) cosmological model in self-creation theory in general relativity and Lyra geometry

  • Original Paper
  • Published:
Indian Journal of Physics Aims and scope Submit manuscript

Abstract

In this paper, we show that no solutions exist for Bianchi type \({\hbox {VI}}_0\) cosmological model in the modified gravity theories, namely in self-creation theory and in gravity theory based on Lyra geometry under the two physical conditions: The pressure p and the density \(\rho\) of the fluid are related by the equation of state \(p=\lambda \rho ,\,\, 0\le \lambda \le 1,\) and the scalar expansion \(\Theta\) of the cosmological model is proportional to the eigenvalue \(\sigma _3^3\) of the shear tensor. In self-creation theory, only the possible solutions are found for dust and radiation cases. Physical and geometrical properties of the obtained models are discussed for different cases of matter distribution. Also, we study the effect of the scalar field \(\phi\) on the entropy \({\mathbf {S}}\) of our universe with an expression for the entropy for all different cases of matter distribution. Also we have proved that the Lyra term has no effect on the entropy of the universe.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. C W Misner Astrophys. J. 151 431 (1968)

    Article  ADS  Google Scholar 

  2. B Saha Phys. Rev. D69 124006 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  3. A Einstein Ann. Phys. (Lpz)49 769 (1916)

    Article  ADS  Google Scholar 

  4. H Weyl Sitzungsber. Preuss. Akad. Wiss. 26 465 (1918)

    Google Scholar 

  5. G Lyra Math. Z54 52 (1951)

    Article  MathSciNet  Google Scholar 

  6. G A Barber Gen. Relativ. Gravit.14 117 (1982)

    Article  ADS  Google Scholar 

  7. C Brans and R H Dicke Phys. Rev.124 925 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  8. G A Barber, arXiv:1009.5862v2. (2010)

  9. L O Pimentel Astrophys. Space Sci.116 395 (1985)

    ADS  MathSciNet  Google Scholar 

  10. H H Soleng Astrophys. Space Sci.139 13 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  11. D R K Reddy and R Venkateswarlu Astrophys. Space Sci.155 135 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  12. R Venkateswarlu and D R K Reddy Astrophys. Space Sci.168 193 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  13. K Shanthi and V U M Rao Astrophys. Space Sci.179 147 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  14. S Ram and C P Singh Astrophys. Space Sci.257 123 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  15. A Pradhan and A K Vishwakarma Int. J. Mod. Phys. D11 1195 (2002)

    Article  ADS  Google Scholar 

  16. U K Panigrahi and R C Sahu Theor. Appl. Mech.30 163 (2003)

    Article  Google Scholar 

  17. R Venkateswarlu, V U M Rao and P Kumar Int. J. Theor. Phys.47 640 (2008)

    Article  Google Scholar 

  18. S M Borkar and N K Ashtankar Tensor73 228 (2013)

    Google Scholar 

  19. S M Borkar and N K Ashtankar Am. J. Mod. Phys.2 261 (2013)

    Article  Google Scholar 

  20. J Jaiswal and R K Tiwari Int. J. Theor. Appl. Sci.5 6 (2013)

    Google Scholar 

  21. S D Katore, R S Rane and V B Kurkure Astrophys. Space Sci.315 347 (2008)

    Article  ADS  Google Scholar 

  22. R Bali and L Poonia International Journal of Modern Physics: Conference Series22 p 593 (World Scientific Publishing Company) (2013)

  23. M K Verma and S Ram Appl. Math.2 348 (2011)

    Article  MathSciNet  Google Scholar 

  24. K S Adhav, A S Bansod, S L Munde and R G Nakwal Astrophys. Space Sci.332 497 (2011)

    Article  ADS  Google Scholar 

  25. S C Priyanka, M K Singh and S Ram Glob. J. Sci. Front. Res.12 83 (2012)

    Google Scholar 

  26. M A Rahman and M Ansari Int. J. Math. Arch. (IJMA)4 210 (2013)

    Google Scholar 

  27. V C Jain and N Jain Prespacetime J.6 273 (2015)

    Google Scholar 

  28. V C Jain and N Jain Int. J. Mod. Sci. Eng. Technol. (IJMSET)1 74 (2015)

    Google Scholar 

  29. K S Thorne Astrophys. Space Sci.148 51 (1967)

    Google Scholar 

  30. G F R Ellis General Relativity and Cosmology (ed.) R K Sachs (Clarendon Press) p 117 (1973)

  31. S W Hawking and G F R Ellis The Large-Scale Structure of Space Time (Cambridge: Cambridge University Press) p 94 (1973)

    Book  Google Scholar 

  32. E A Hegazy Iran. J. Sci. Technol. Trans. A Sci.43 663–669 (2019). https://doi.org/10.1007/s40995-018-0530-z

    Article  MathSciNet  Google Scholar 

  33. K Bamba, S Capozziello, S I Nojiri and S D Odintsov Astrophys. Space Sci.342(1) 155 (2012)

    Article  ADS  Google Scholar 

  34. R G Cai and S P Kim J. High Energy Phys.02 050 (2005)

    Article  ADS  Google Scholar 

  35. H Ebadi and H Moradpour Int. J. Mod. Phys. D24 14 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

FR would like to thank the authorities of the Inter-University Centre for Astronomy and Astrophysics, Pune, India, for providing research facilities. FR is also grateful to DST-SERB and DST-PURSE, Government of India, for financial support.

Author information

Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Minia University, El-Minia, 61519, Egypt

    E. A. Hegazy

  2. Department of Mathematics, Jadavpur University, Kolkata, West Bengal, 700032, India

    Farook Rahaman

Authors
  1. E. A. Hegazy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farook Rahaman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. A. Hegazy.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hegazy, E.A., Rahaman, F. Bianchi type \({\hbox {VI}}_0\) cosmological model in self-creation theory in general relativity and Lyra geometry. Indian J Phys 93, 1643–1650 (2019). https://doi.org/10.1007/s12648-019-01424-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12648-019-01424-8

Keywords

PACS Nos.

Search

Navigation