Viscous cosmologies

Abstract

We probe into universes filled with quark gluon plasma with non-zero viscosities. In particular, we study the evolution of a universe with non-zero shear viscosity motivated by the theoretical result of a non-vanishing shear viscosity in the quark gluon plasma due to quantum-mechanical effects. We first review the consequences of a non-zero bulk viscosity and show explicitly the non-singular nature of the bulk-viscosity-universe by calculating the cosmological scale factor which goes to zero only asymptotically. The cosmological model with bulk viscosity is extended to include a cosmological constant. The previous results are contrasted with the cosmology with non-zero shear viscosity. We first clarify under which conditions shear viscosity terms are compatible with the Friedmann–Lamaître–Robertson–Walker metric. To this end we use a version of the energy–momentum tensor from the Müller–Israel–Stewart theory which leads to causal Navier–Stoke equations. We then derive the corresponding Friedmann equations and show under which conditions the universe emerges to be non-singular.