Local equilibrium solutions in simple anisotropic cosmological models, as described by relativistic fluid dynamics

TL;DR

This paper investigates the applicability of Israel-Stewart thermodynamics in anisotropic cosmological models, finding that only fluids with zero bulk viscosity approach local thermal equilibrium, and that truncated equations can produce unphysical solutions.

Contribution

It provides a dynamical systems analysis of viscous cosmological models, highlighting limitations of truncated Israel-Stewart equations and clarifying conditions for local thermal equilibrium.

Findings

Only fluids with zero bulk viscosity reach local thermal equilibrium.

Truncated Israel-Stewart equations can produce pathological and initial-condition sensitive solutions.

Full Israel-Stewart theory remains physically relevant under specific conditions.

Abstract

We test the physical relevance of the full and the truncated versions of the Israel-Stewart theory of irreversible thermodynamics in a cosmological setting. Using a dynamical systems method, we determine the asymptotic future of plane symmetric Bianchi type I spacetimes with a viscous mathematical fluid, keeping track of the magnitude of the relative dissipative fluxes, which determines the applicability of the Israel-Stewart theory. We consider the situations where the dissipative mechanisms of shear and bulk viscosity are involved separately and simultaneously. It is demonstrated that the only case in the given model when the fluid asymptotically approaches local thermal equilibrium, and the underlying assumptions of the Israel-Stewart theory are therefore not violated, is that of a dissipative fluid with vanishing bulk viscosity. The truncated Israel-Stewart equations for shear viscosity are found to produce solutions which manifest pathological dynamical features and, in addition, to be strongly sensitive to the choice of initial conditions. Since these features are observed already in the case of an oversimplified mathematical fluid model, we have no reason to assume that the truncation of the Israel-Stewart transport equations will produce relevant results for physically more realistic fluids. The possible role of bulk and shear viscosity in cosmological evolution is also discussed.