Generalised equilibrium of cosmological fluids in second-order thermodynamics

Combining the second-order entropy flow vector of the causal Israel-Stewart theory with the conformal Killing-vector property of $u_{i}/T$, where $u_{i}$ is the four-velocity of the medium and T its equilibrium temperature, we investigate generalized equilibrium states for cosmological fluids with nonconserved particle number. We calculate the corresponding equilibrium particle production rate and show that this quantity is reduced compared with the results of the previously studied first-order theory. Generalized equilibrium for massive particles turns out to be compatible with a dependence $\rho \propto a ^{-2}$ of the fluid energy density $\rho$ on the scale factor a of the Robertson-Walker metric and may be regarded as a realization of so-called K-matter.