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Cosmology with a nonlinear barotropic Israel-Stewart fluid with causal relaxation time

Vishnu A Pai ^* and Titus K Mathew ^†

Department of Physics, Cochin University of Science and Technology, Cochin-682022, Kerala, India

^*Contact author: vishnuajithj@gmail.com, vishnuajithj@cusat.ac.in
^†Contact author: titus@cusat.ac.in

Phys. Rev. D 113, 063560 – Published 24 March, 2026

DOI: https://doi.org/10.1103/pyht-c2jt

Abstract

We derive an extended expression for the relaxation time of a barotropic Israel-Stewart (IS) fluid (BISF) using the nonlinear causality constraint, and propose a new formulation for modeling causal bulk viscous dissipation in barotropic fluids in the full nonlinear regime. With this generalized relaxation time, the covariant nonlinear IS equation reduces to a first-order nonlinear differential equation relating the bulk viscous pressure and the energy density, which remains valid in any homogeneous and isotropic spacetime. In a spatially flat Friedmann universe, adopting this extended relation within the generalized nonlinear IS theory yields a new class of analytical solutions in both the linear and certain truncated nonlinear regimes. We also find that the resulting effective equation of state in the linear regime naturally reproduces the generalized polytropic form often introduced phenomenologically in the literature. The dynamical implications of adopting the causal relaxation time for BISF are investigated in the linear, truncated nonlinear, and full nonlinear far-from-equilibrium regimes, and the constraints required to ensure physically viable evolution of the viscous fluid are derived. A detailed dynamical systems analysis of the coupled Einstein-Israel–Stewart (EIS) system is also performed. Finally, we solve the coupled EIS equations numerically in the full nonlinear regime 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.

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