On a viable first order formulation of relativistic viscous fluids and its applications to cosmology

We consider a first order formulation of relativistic fluids with bulk viscosity based on a stress-energy tensor introduced by Lichnerowicz. Choosing a barotropic equation of state, we show that this theory satisfies basic physical requirements and, under the further assumption of vanishing vorticity, that the equations of motion are causal, both in the case of a fixed background and when the equations are coupled to Einstein's equations. Furthermore, Lichnerowicz's proposal does not fit into the general framework of first order theories studied by Hiscock and Lindblom, and hence their instability results do not apply. These conclusions apply to the full-fledged non-linear theory, without any equilibrium or near equilibrium assumptions. Similarities and differences between the approach here explored and other theories of relativistic viscosity, including the Mueller-Israel-Stewart formulation, are addressed. Cosmological models based on the Lichnerowicz stress-energy tensor are studied. Finally, it is also shown how the present model can be generalized to a second order formulation.