  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.
