The Mass of Graviton and Its Relation to the Number of Information according to the Holographic Principle

Abstract

We investigate the relation of the mass of the graviton to the number of information N in a flat universe. As a result we find that the mass of the graviton scales as $m_{\text{gr}}\propto 1/\sqrt{N}$ . Furthermore, we find that the number of gravitons contained inside the observable horizon is directly proportional to the number of information N; that is, N _gr ∝ N. Similarly, the total mass of gravitons that exist in the universe is proportional to the number of information N; that is, $M_{\text{gr}}\propto \sqrt{N}$ . In an effort to establish a relation between the graviton mass and the basic parameters of the universe, we find that the mass of the graviton is simply twice the Hubble mass m _H as it is defined by Gerstein et al. (2003), times the square root of the quantity q − 1/2, where q is the deceleration parameter of the universe. In relation to the geometry of the universe we find that the mass of the graviton varies according to the relation $m_{\text{gr}}\propto \sqrt{R_{\text{sc}}}$ , and therefore m _gr obviously controls the geometry of the space time through a deviation of the geodesic spheres from the spheres of Euclidean metric.