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Indian Journal of Physics

, Volume 93, Issue 12, pp 1643–1650 | Cite as

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

  • E. A. HegazyEmail author
  • Farook Rahaman
Original Paper

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.

Keywords

Lyra geometry Einstein field equations Bianchi type \({\hbox {VI}}_0\) cosmological models Self-creation theory Scalar expansion Entropy 

PACS Nos.

04.20.-q 

Notes

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.

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Copyright information

© Indian Association for the Cultivation of Science 2019

Authors and Affiliations

  1. 1.Mathematics Department, Faculty of ScienceMinia UniversityEl-MiniaEgypt
  2. 2.Department of MathematicsJadavpur UniversityKolkataIndia

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