A violation of the covariant entropy bound?

Abstract: Several arguments suggest that the entropy density at high energy density $\rho$ should be given by the expression $s=K\sqrt{\rho/G}$, where $K$ is a constant of order unity. On the other hand the covariant entropy bound requires that the entropy on a light sheet be bounded by $A/4G$, where $A$ is the area of the boundary of the sheet. We find that in a suitably chosen cosmological geometry, the above expression for $s$ violates the covariant entropy bound. We consider different possible explanations for this fact; in particular the possibility that entropy bounds should be defined in terms of volumes of regions rather than areas of surfaces.