Nonlocal extension of causal thermodynamics of the isotropic cosmic fluid

TL;DR

This paper extends the Israel-Stewart causal thermodynamics model for the cosmic fluid to include nonlocal effects, deriving a new master equation analogous to the Burgers equation and analyzing exact solutions.

Contribution

It introduces a nonlocal generalization of the Israel-Stewart model for relativistic thermodynamics of the cosmic fluid, deriving a novel integro-differential equation.

Findings

Derived the nonlocal master equation for the cosmic fluid's nonequilibrium pressure.

Reduced the integro-differential equation to a second-order differential equation.

Presented two exact solutions of the nonlinear key equation.

Abstract

We establish the nonlocal generalization of the Israel-Stewart model for the relativistic causal thermodynamics of the cosmic fluid, which evolves in the homogeneous isotropic Universe. Based on the second law of thermodynamics we derive the integro-differential master equation for the nonequilibrium pressure scalar and reduce it to the differential equation of the second order in time derivatives. We show that this master equation can be considered as the relativistic analog of the Burgers equation, which is known in the classical theory of viscoelasticity. We obtain the nonlinear key equation, which contains the energy density scalar only, and analyze two exact solutions of the model. The effective temperature is considered to be associated with the barotropic equation of state of the cosmic fluid.