Bianchi Type-II Cosmological Model with Viscous Fluid

TL;DR

This paper derives exact solutions for a Bianchi type-II cosmological model considering shear and bulk viscosity, exploring how viscosity influences the universe's evolution under specific conditions.

Contribution

It provides new exact solutions for viscous Bianchi type-II models and analyzes the effects of viscosity on cosmological dynamics.

Findings

Exact solutions for viscous and perfect fluid cases

Viscosity influences the evolution of the cosmological model

Barotropic equation of state emerges naturally in certain cases

Abstract

A spatially homogeneous and locally rotationally symmetric Bianchi type-II cosmological model under the influence of both shear and bulk viscosity has been studied. Exact solutions are obtained with a barotropic equation of state between thermodynamics pressure and the energy density of the fluid, and considering the linear relationships amongst the energy density, the expansion scalar and the shear scalar. Special cases with vanishing bulk viscosity coefficients and with the perfect fluid in the absence of viscosity have also been studied. The formal appearance of the solutions is the same for both the viscous as well as the perfect fluids. The difference is only in choosing a constant parameter which appears in the solutions. In the cases of either a fluid with bulk viscosity alone or a perfect fluid, the barotropic equation of state is no longer an additional assumption to be imposed; rather it follows directly from the field equations.