#### Document Type

Article

#### Publication Date

2013

#### Department

Department of Physics and Computer Science

#### Abstract

Bekenstein has obtained is an upper limit on the entropy *S*, and from that, an information number bound *N* is deduced. In other words, this is the information contained within a given finite region of space that includes a finite amount of energy. Similarly, this can be thought as the maximum amount of information required to perfectly describe a given physical system down to its quantum level. If the energy and the region of space are finite then the number of information *N* required in describing the physical system is also finite. In this short letter two information number bounds are derived and compared for two types of universe. First, a universe without a cosmological constant lamda and second a universe with a cosmological constant lamda *Λ* are investigated. This is achieved with the derivation of two different relations that connect the Hubble constant and cosmological constants to the number of information *N*. We find that the number of information N involved in a the two universes are identical or *N*_{2} = *N*_{2Λ} , and that the total mass of the universe scales as the square root of the information number *N*, containing. an information number *N* of the order of 10^{122} . Finally, we expressed Calogero’s quantization action as a function of the number of information *N*. We also have found that in self-gravitating systems the number of information *N* in nats is the ratio of the total kinetic to total thermal energy of the system.

#### Recommended Citation

Haranas, I., Gkigkitzis, I. Bekenstein Bound of Information Number N and its Relation to Cosmological Parameters in a Universe with and without Cosmological Constant. Modern Physics Letters A 28:19 (2013). DOI: 10.1142/S0217732313500776

## Comments

This article was originally published in

Modern Physics Letters A, 28(19).Reproduced with permission.