Abstract A model of a cloud formed by massive strings is used as a source of Bianchi type II cases. We assume that the expansion (θ) in the model is proportional to the shear (σ). To get an exact solution, we consider the equation of state of the fluid to be in the stiff form. It is found that the bulk viscosity played a very important role in the history of the universe. In the presence of bulk viscosity the particles dominate over strings whereas in the absence of it, strings dominate over the particles, which is not consistent with recent observations. Also we observe that the viscosity causes the expansion of the universe to be accelerating. Our models are evolving from an early decelerating phase to a late time accelerating phase. The physical and geometrical behaviors of these models are discussed.

Keywords cosmology: theory — viscous fluid — massive string

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