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

TL;DR

The paper addresses the problem of modeling causal bulk viscosity in relativistic cosmology beyond near-equilibrium. It derives a generalized relaxation time $\tau_c$ from a nonlinear causality constraint and embeds it in a barotropic BISF, reducing the nonlinear Israel–Stewart equation to a first-order nonlinear relation between the bulk viscous pressure $\Pi$ and the energy density $\rho$ in FLRW spacetimes. It presents exact analytical solutions in the linear regime for general $n$ and analytical nonlinear solutions for the $n=0$ case via Bessel/Gamma functions, complemented by a dynamical-systems analysis showing a line of unstable early-time fixed points and a stable late-time attractor. The work further demonstrates a transient viscous-driven slow-roll expansion that naturally exits into a radiation-dominated epoch, aligning with observational constraints and offering a robust framework for far-from-equilibrium viscous cosmology with broad applications in early-universe physics, QGP, and neutron-star dynamics.

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.

Figures (8)

• Figure 1: This is a 4D scatter plot depicting the evolution of $\Pi/\rho$ with three different parameters, corresponding to $n=0$ case of BISF in the linear regime.
• Figure 2: These are 4D scatter plots showing the evolution of $\Pi/\rho$ with three different parameters, for $n\neq0$ case of BISF in the linear regime.
• Figure 3: These are contour plots showing the evolution of $\Pi/\rho$ with three different parameters, for $n\neq0$ case.
• Figure 4: Scatter plot depicting the evolution of $\Pi/\rho$ with 3 model parameters, for linear, $n=0$ case of BISF.
• Figure 5: Plot depicting the evolution of $\Pi/\rho$ with energy density, for $\Lambda_e=1, \epsilon=0.01, \eta=4.15$ and three different $\lambda$ values. Dotted dashed red line is for $\Pi/\rho=-4/3$.