  The holographic principle in a radiation dominated universe, as discussed
first by Verlinde (2000), is extended so as to incorporate the case of a
bulk-viscous cosmic fluid. This corresponds to a non-conformally invariant
theory. Generalization of the Cardy-Verlinde entropy formula to the viscous
case appears to be formally possible, although on physical grounds one may
question some elements in this type of theory, especially the manner in which
the Casimir energy is evaluated. Also, we consider the observation made by Youm
(2002),namely that the entropy of the universe is no longer expressible in the
conventional Cardy-Verlinde form if one relaxes the radiation dominance
equation of state for the fluid and instead merely assumes that the pressure is
proportional to the energy density. We show that Youm's generalized entropy
formula remains valid when the cosmic fluid is no longer ideal, but endowed
with a constant bulk viscosity. In the introductory part of this article, we
take a general point of view and survey the essence of cosmological theory
applied to a fluid containing both a constant shear viscosity and a constant
bulk viscosity.
