  The intention of this paper is mainly two-fold. \textit{First}, we point out
a striking numerical agreement between the bulk viscosity in the lepton era
calculated by Husdal (2016) and our own calculations of the present-day bulk
viscosity when the functional form is $\zeta\,\sim\sqrt{\rho}$. From a
phenomenological point of view, we thus seem to have an ansatz for the
viscosity which bridges the infancy of the Universe ($\sim 1$ s) with the
present. This can also be looked upon as a kind of symmetry between the
early-time cosmology and the present-day cosmology: it is quite remarkable that
the kinetic theory-based bulk viscosity in the early universe and the
experimentally-based bulk viscosity in the present universe can be covered by
the same simple analytical formula. \textit{Second}, we consider the Kasner
universe as a typical anisotropic model of Bianchi-type I, investigating
whether this geometrical model is compatible with constant viscosity
coefficients in the fluid. Perhaps surprisingly, the existence of a shear
viscosity turns out to be incompatible with the Kasner model. By contrast, a
bulk viscosity is non-problematic in the {\it isotropic} version of the model.
In the special case of a Zel'dovich (stiff) fluid, the three equal exponents in
the Kasner metric are even determined by the bulk viscosity alone, independent
of the value of the fluid energy density. We also give a brief comparison with
some other recent approaches to viscous cosmology.
