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Bekenstein has obtained is an upper limit on the entropy S, and from that, aninformation number bound N is deduced. In other words, this is the informationcontained within a given finite region of space that includes a finite amountof energy. Similarly, this can be thought as the maximum amount of informationrequired to perfectly describe a given physical system down to its quantumlevel. If the energy and the region of space are finite then the number ofinformation N required in describing the physical system is also finite. Inthis short letter two information number bounds are derived and compared fortwo types of universe. First, a universe without a cosmological constant lamdaand second a universe with a cosmological constant lamda are investigated. Thisis achieved with the derivation of two different relations that connect theHubble constant and cosmological constants to the number of information N. Wefind that the number of information N involved in a the two universes areidentical or  N1=N2, and that the total mass of the universe scales as the square root ofthe information number N, containing an information number N of the order of10E+122. Finally, we expressed Calogero quantization action as a function ofthe number of information N. We also have found that in self gravitatingsystems the number of information N in nats is the ratio of the total kineticto total thermal energy of the system.

Bekenstein Bound of Information Number N and its Relation to Cosmological Parameters in a Universe with and without Cosmological Constant