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

TL;DR

This paper explores the Bekenstein bound on information in the universe, deriving relations between cosmological parameters and information content, and finds that the universe's total information is approximately 10^122, regardless of the presence of a cosmological constant.

Contribution

The paper derives two bounds on the information number for universes with and without a cosmological constant and relates these bounds to cosmological parameters and total mass.

Findings

The information number N is approximately 10^122 for both universe types.

The total mass of the universe scales as the square root of N.

In self-gravitating systems, N relates to kinetic and thermal energies.

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 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 N1=N2, 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 10E+122. Finally, we expressed Calogero 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.