Non-Archimedean Algebra: Applications to Cosmology and Gravitation

Application of recently developed non-Archimedean algebra to a flat and finite universe of total mass M ₀ and radius R ₀ is described. In this universe, mass m of a body and distance R between two points are bounded from above, i.e., 0mM ₀, 0RR ₀. The universe is characterized by an event horizon at R ₀ (there is nothing beyond it, not even space). The radial distance metric is compressed toward horizon, which is shown to cause the phenomenon of red shift. The corresponding modified Minkowski's metric and Lorentz transforms are obtained. Applications to Newtonian gravity shows a weakening at large scales (RR ₀) and a regular behavior as R0.