Relationship between two theories of dissipative relativistic hydrodynamics applied to cosmology

We compare Israel's relativistic causal theory of transient effects with the relativistic extended irreversible thermodynamics of Pav\'on, Jou, and Casas-Vasqu\`ez, applying both to the case of cosmic fluid with bulk viscosity only. They are completely equivalent up to the first order in the parameter characterizing the departure from equilibrium. We show, if certain relations between the main variables of the two theories hold, that they are also equivalent up to the second order in this parameter. We also extend up to any order Israel's theory and give the relations permitting again the equivalence between the two theories in this general case. Some cosmological consequences are discussed.