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.

• Received 3 February 2015

DOI:https://doi.org/10.1103/PhysRevD.91.084058