A violation of the covariant entropy bound?

TL;DR

This paper examines whether the high-energy entropy density formula conflicts with the covariant entropy bound in cosmological settings, suggesting potential need to redefine entropy bounds in terms of volumes.

Contribution

It demonstrates a specific cosmological scenario where the entropy density formula violates the covariant entropy bound, challenging existing theoretical assumptions.

Findings

Entropy density at high energy density can violate the covariant entropy bound.

The violation depends on the choice of cosmological geometry.

Alternative definitions of entropy bounds may be necessary.

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.