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Bianchi type-III bulk viscous and barotropic perfect fluid cosmological models in Lyra’s geometry. (English) Zbl 1213.83079
Summary: We have investigated Bianchi type III bulk viscous and barotropic perfect fluid cosmological models in the frame work of Lyra’s geometry. To get deterministic models of universe, we have assumed the three conditions: (i) shear scalar $\left(\sigma \right)$ is proportional to the expansion $\left(\theta \right)$. This leads to $B={C}^{n}$, where $B$ and $C$ are metric potentials. (ii) In presence of viscous fluid, the coefficient of viscosity of dissipative fluid is a power function of mass density $\xi ={\xi }_{0}{\rho }^{m}$, where ${\xi }_{0}$ and $m$ are constant and (iii) in absence of viscosity, a proportionality relation between pressure and energy density of barotropic perfect fluid $p=\alpha \rho$, where $\alpha$ is a proportionality constant. In all the cases, we observed that the displacement vector $\beta$ is large at beginning of the universe and reduces fast during its evolution so that its nature coincide with the behavior of cosmological constant ${\Lambda }$.
##### MSC:
 83C55 Macroscopic interaction of the gravitational field with matter (general relativity) 83D05 Relativistic gravitational theories other than Einstein’s 83F05 Relativistic cosmology 83C15 Closed form solutions of equations in general relativity