On the anisotropic bouncing universe with viscosity

Abstract

We investigate the role of bulk and shear viscosity in the spatially homogeneous anisotropic spacetime, in particular, the Kantowski–Sachs (KS) spacetime. General conditions for the bouncing evolution of universe in anisotropic background have been obtained by using the derived propagation equations of expansion scalar, shear scalar and spatial 3-curvature. We show that the presence of shear viscosity in the model prohibits the energy density to attain its extremum in the bouncing model. We explore the qualitative behavior of KS cosmologies by formulating the Einstein’s field equations into a plane-autonomous system of equations by taking dimensionless equation of state. The stability of the system has been investigated by evaluating and analyzing the eigenvalues at the critical points. The stable solutions exist for the system composed of bulk and shear viscosity. The present analysis through dynamical system method illustrates that the universe does not exhibit synchronous bounce with perfect fluid and/or viscous fluids in the KS spacetime.