Equations of state and transport equations in viscous cosmological models

Abstract

The aim of this paper is to compare the evolution of viscous cosmological models for three different constitutive equations for the viscous pressure $\sigma$, namely: Eckart theory ($\sigma =-\xi {\nabla }_{\mu }{u}^{\mu }$), Maxwell-Cattaneo theory ($\sigma +\tau \dot{\sigma }=-\xi {\nabla }_{\mu }{u}^{\mu }$), and generalized second-order Israel-Stewart theory ($\sigma +\tau \dot{\sigma }=-\xi {\nabla }_{\mu }{u}^{\mu }-\frac{1}{2}\xi \sigma T\rho u^{\mu }{\nabla }_{\mu }\left(\frac{v\tau }{T\xi }\right)$). In the last case, the nonlinear terms may be interpreted as a consequence of nonlinear equations of state for absolute temperature and thermodynamic pressure. We show that the nonlinear terms of the latter equation are compatible with a viscosity-driven inflationary expansion.