On the feasibility of truncated Israel-Stewart model in the context of late acceleration

Abstract: A dissipative model of the Universe based on the causal relativistic truncated Israel-Stewart theory is analysed in the context of recent accelerated expansion of the Universe. The bulk viscosity and relaxation time are taken as $\xi=\alpha\rho^s$ and $\tau=\frac{\alpha}{\epsilon\gamma(2-\gamma)}\rho^{s-1}$ respectively. For $s=1/2,$ we found an analytical solution for the Hubble parameter of the model. We have estimated the model parameters by treating $\gamma=1$ and $\gamma$ as a free parameter using the latest cosmological data. The model predicts a prior decelerated phase and an end de Sitter phase as in the standard $\Lambda$CDM model. The dynamical system analysis shows that the prior decelerated epoch is an unstable equilibrium, while the far future de Sitter epoch is stable. The age of the Universe obtained around $13.66$ Gyr, which is close to the recent observations. The second law of thermodynamics is found to be satisfied throughout the evolution in this model. The feasibility of the model has been checked by contrasting with models based on the full Israel-Stewart and the Eckart viscous theories. The truncated viscous model appears more compatible with astronomical observations than the Eckart and full causal viscous models.