  The holographic principle is studied in the context of a $n+1$ dimensional
radiation dominated closed Friedman-Robertson-Walker (FRW) universe. The
radiation is represented by a conformal field theory with a large central
charge. Following recent ideas on holography, it is argued that the entropy
density in the early universe is bounded by a multiple of the Hubble constant.
The entropy of the CFT is expressed in terms of the energy and the Casimir
energy via a universal Cardy formula that is valid for all dimensions. A new
purely holographic bound is postulated which restricts the sub-extensive
entropy associated with the Casimir energy. Unlike the Hubble bound, the new
bound remains valid throughout the cosmological evolution. When the new bound
is saturated the Friedman equation exactly coincides with the universal Cardy
formula, and the temperature is uniquely fixed in terms of the Hubble parameter
and its time-derivative.

High Energy Physics - Theory