  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.
