  The holographic bound states that the entropy in a region cannot exceed one
quarter of the area (in Planck units) of the bounding surface. A version of the
holographic principle that can be applied to cosmological spacetimes has
recently been given by Fischler and Susskind. This version can be shown to fail
in closed spacetimes and they concluded that the holographic bound may rule out
such universes. In this paper I give a modified definition of the holographic
bound that holds in a large class of closed universes. Fischler and Susskind
also showed that the dominant energy condition follows from the holographic
principle applied to cosmological spacetimes with $a(t)=t^p$. Here I show that
the dominant energy condition can be violated by cosmologies satisfying the
holographic principle with more general scale factors.
