Bianchi type $${\hbox {VI}}_0$$VI0 cosmological model in self-creation theory in general relativity and Lyra geometry

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.