## 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 $$(\sigma)$$ is proportional to the expansion $$(\theta)$$. 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 (hydrodynamics, etc.) 83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories 83F05 Relativistic cosmology 83C15 Exact solutions to problems in general relativity and gravitational theory
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