Cosmology with non-linear barotropic Israel-Stewart fluid with causal relaxation time

Abstract: We derive an extended expression for the relaxation time of a barotropic Israel-Stewart (IS) fluid using the non-linear causality constraint, and propose a new formulation for modeling causal viscous dissipation in barotropic fluids. With this generalized relaxation time, the non-linear IS equation simplifies to a first-order non-linear expression connecting bulk viscous pressure and energy density, which remains valid in any homogeneous and isotropic spacetime. In the case of spatially flat Friedmann universe, adopting this extended relation in the generalized non-linear IS theory, provides new class of analytical solutions in both, the linear, and the non-linear regimes. We also find that, the resulting effective equation of state in the linear regime naturally reproduces the generalized polytropic form which is often introduced phenomenologically in literature. Resulting dynamical implications are investigated and the constraints necessary for ensuring an acceptable evolutionary behavior for the fluid are determined. A detailed dynamical system analysis of the coupled Einstein-Israel-Stewart (EIS) system is also performed. Finally, we solve the coupled EIS equations numerically, and show that the model can support a transient Hubble slow-roll expansion phase with a smooth exit to a radiation-dominated universe, which is challenging to obtain in standard inflationary models.