I have a question about the Bekenstein bound or the holographic principle.
I make the following assumptions:
- The universe is infinite
- The universe is homogeneous
These assumptions are at least considered plausible (on large scale). The Bekenstein bound (or holographic principle) say that the information contained in a ball of radius $R$ is at most $q A$ where $q$ is a proportionality constant and $A$ the area of the sphere. But if the universe is homogeneous, its density is constant and so the information contained in a sphere should be proportional to $R^3$; while the bound is proportional to $R^2$. That seems impossible, a big enough sphere will eventually exceed the bound.
A similar argument seems to imply that some sufficiently large portion of the universe should necessarily be a black hole.
What I am doing wrong here?