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 . 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, . 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 , 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.