Dynamical system analysis and thermal evolution of the causal dissipative model

Abstract: The dynamical system behaviour and thermal evolution of a homogeneous and isotropic dissipative universe are analyzed. The dissipation is driven by the bulk viscosity $\xi = \alpha \rho^s $ and the evolution of bulk viscous pressure is described using the full causal Israel-Stewart theory. We find that for $s=1/2$ the model possesses a prior decelerated epoch which is unstable and a stable future accelerated epoch. From the thermodynamic analysis, we have verified that the local as well as the generalised second law of thermodynamics are satisfied throughout the evolution of the universe. We also show that the convexity condition $S''<0$ is satisfied at the end stage of the universe which implies an upper bound to the evolution of the entropy. For $s\neq1/2,$ the case $s<1/2$ is ruled out since it does not predict the conventional evolutionary stages of the universe. On the other hand, the case $s>1/2$ does imply a prior decelerated and a late de Sitter epochs, but both of them are unstable fixed points. The thermal evolution corresponding to the same case implies that GSL is satisfied at both the epochs but convexity condition is violated by both, so that entropy growth is unbounded. Hence for $s>1/2$ the model does not give a stable evolution of the universe.