De Sitter-Invariant Special Relativity and Galaxy Rotation Curves

Abstract

Owing to the existence of an invariant length at the Planck scale, Einstein’s special relativity breaks down at that scale. A possible solution to this problem is arguably to replace the Poincaré-invariant Einstein special relativity with a de Sitter-invariant special relativity. In addition to reconciling Lorentz symmetry with the existence of an invariant length, such replacement produces concomitant changes in all relativistic theories, including general relativity, which becomes what we have called de Sitter modified general relativity. In this paper, the Newtonian limit of this theory is used to study the circular velocity of stars around the galactic center. It is shown that the de Sitter modified Newtonian force—which includes corrections coming from the underlying local kinematics—could possibly explain the rotation curves of galaxies without the necessity to suppose the existence of a dark matter halo.