Brane viscous cosmology in the plasma era

Abstract

We consider how the five-dimensional Randall-Sundrum (one-brane) theory becomes modified when account is taken of the bulk viscosity of the cosmic fluid on the brane. We focus on the plasma era between $10^{12}$K (muon pair annihilation) to about $5\times 10^9$K (electron-positron annihilation), which includes the first order quark-hadron transition beginning at an energy density of about $5\times 10^9\rm MeV^4$. Various possibilities are examined for modeling the bulk viscosity, preference being at the end given to the results calculated from relativistic kinetic theory. According to this, the viscosity is negligible at the highest temperatures, but may amount to a few per cent corrections in the later stages of the plasma era. We also briefly consider anisotropic universes where the shear viscosity comes into play, and show that in the case of the Kasner model the influences from bulk viscosity and shear viscosity become comparable when the anisotropy parameter of the universe is of order $A \sim 10^{-11} $ in the beginning of the plasma era, and $A \sim 10^{-2}$ in its later region.