Geometry of the Universe and Its Relation to Entropy and Information

In an effort to investigate a possible relation between geometry and information, we establish a relation of the Ricci scalar in the Robertson-Walker metric of the cosmological Friedmann model to the number of information and entropy . This is with the help of a previously derived result that relates the Hubble parameter to the number of information . We find that the Ricci scalar has a dependence which is inversely proportional to the number of information and entropy . Similarly, a nonzero number of information would imply a finite Ricci scalar, and therefore space time will unfold. Finally, using the maximum number of information existing in the universe, we obtain a numerical value for the Ricci scalar to be . 1. Introduction Any physical system can register information just because it exists. Those systems that evolve dynamically in time not only transform but also process the information. In relation to the laws of physics, we say that these laws determine the amount of information that a given system can register (i.e., number of bits or nats) as well as the number of elementary logic operations that the given system can perform (i.e., numbers of operations). In his original paper, Landauer [1] made the statement that information is physical, and then he went on stating that: first, information is registered and processed by physical systems, and second, all physical systems register and process information. Physical systems can be described in terms of information, but information processing is related to the system description by physical laws. In relation to the universe in a recent paper by Haranas and Gkigkitzis [2, 3], the authors investigate the Bekenstein [4] bound of information number and its relation to cosmological parameters in a universe with and without cosmological constant, and they also derive a relation that describes the dependence of Hubble parameter on the amount of information . The authors derive that Hubble’s parameter at any time in the history of the universe can be written in the following way [3]: where , ？m, ？s is the Planck length and Planck time, is the speed of light, and is the number of information in nats. In this paper, is an effort to establish a possible relation between geometry and information. For that, we start by investigating the relation of the Ricci scalar derived from a Robertson-Walker metric in the Friedmann cosmological model to the number of information bit . We also investigate the relation of the Ricci scalar to entropy . Finally, we use Landauer's principle of information and derive various