Remarks on the viscosity concept in the early universe

Abstract

Some aspects of viscous cosmological models, mainly of Bianchi type-I, are studied, in particular with the purpose of trying to obtain a natural explanation of why the entropy per baryon in the universe,σ ~ 109, is so large. Using the FRW metric it is first shown, in agreement with previous workers, that the expressions for the bulk viscosity as derived from kinetic theory in the plasma era is incapable of explaining the large value ofσ. However it is possible to imagine the viscosity to be an “impulse” viscosity operative in one or several phase transitions in the early universe. This is the main idea elaborated on in the present paper. It is shown that in thek = 0 FRW space, an impulse bulk viscosity ςinfl ~ 1060 g cm−1 s−1) acting at the phase transition at the end of the inflationary epoch corresponds to the correct entropy. If the space is anisotropic, it is natural to exploit the analogy with classical fluid dynamics to introduce the turbulent viscosity concept. This is finally discussed, in relation to an anisotropy introduced in the universe via the Kasner metric.