Crossing the phantom divide with dissipative normal matter in the Israel–Stewart formalism

Abstract

A phantom solution in the framework of the causal Israel-Stewart (IS) formalism is discussed. We assume a late time behavior of the cosmic evolution by considering only one dominant matter fluid with viscosity. In the model it is assumed a bulk viscosity of the form $\xi= \xi_{0}\rho^{1/2}$, where $\rho$ is the energy density of the fluid. We evaluate and discuss the behavior of the thermodynamical parameters associated to this solution, like the temperature, rate of entropy, entropy, relaxation time, effective pressure and effective EoS. A discussion about the assumption of near equilibrium of the formalism and the accelerated expansion of the solution is presented. The solution allows to cross the phantom divide without evoking an exotic matter fluid and the effective EoS parameter is always lesser than $-1$ and time independent. A future singularity (big rip) occurs, but different from the Type I (big rip) solution classified in S. Nojiri, S. D. Odintsov and S. Tsujikawa, Phys. Rev. D 71, 063004 (2005), if we consider others thermodynamics parameters like, for example, the effective pressure in the presence of viscosity or the relaxation time.