Nonequilibrium relativistic thermodynamics in bulk viscous cosmology

Three different approaches to the relativistic thermodynamics of imperfect fluids are compared: the second-order causal theory of Israel and Stewart (IS), the phenomenological extension of the IS theory proposed by Maartens and Méndez (MM), and the recently developed GENERIC formalism of Grmela and Öttinger. All theories are applied to the case of dissipative cosmology, with bulk viscosity as the only dissipative phenomenon. The MM theory as well as GENERIC give an upper bound on the bulk viscous stress, whereas there is none in the IS theory. In a flat Robertson-Walker universe, the relationship between the different approaches is illustrated for the special case of a relativistic Boltzmann gas. Far away from equilibrium we find qualitatively different behavior, indicating that care should be taken when using the IS theory in this regime.