Bulk viscous Bianchi type I cosmological model in Lyra geometry and in the general theory of relativity

Abstract

In the framework of the gravitational theory based on Lyra geometry and the general theory of relativity, we study Bianchi type I cosmological model in the presence of viscous fluid. A discussion about the suitability of the Sen equations as field equations in Lyra geometry is given. A clear physical meaning for the time component of the displacement vector, introduced in the Sen field equations used in the framework of Lyra geometry, is given by identifying it as a part of the energy momentum tensor (viscosity term). Exact solution of the Einstein field equations is given by assuming the model has a constant deceleration parameter. Moreover, we study the effect of the viscosity term on the entropy of the universe. A formula for calculating the entropy in the presence of viscosity is given by a combination between the second law of thermodynamics and the energy momentum tensor in a conservative manner. We calculate and study the thermodynamic functions (Enthalpy, Gibbs energy and Helmholtz energy) of the universe in the presence of viscosity in Lyra geometry and in the general theory of relativity. The physical and geometrical properties of the obtained models are discussed.