Dark energy and extending the geodesic equations of motion: its construction and experimental constraints

Abstract

With the discovery of Dark Energy, ΛDE, there is now a universal length scale, \({\ell_{\rm DE}=c/(\Lambda_{\rm DE} G)^{1/2}}\), associated with the universe that allows for an extension of the geodesic equations of motion. In this paper, we will study a specific class of such extensions, and show that contrary to expectations, they are not automatically ruled out by either theoretical considerations or experimental constraints. In particular, we show that while these extensions affect the motion of massive particles, the motion of massless particles are not changed; such phenomena as gravitational lensing remain unchanged. We also show that these extensions do not violate the equivalence principal, and that because \({\ell_{\rm DE}=14010^{800}_{820}}\) Mpc, a specific choice of this extension can be made so that effects of this extension are not be measurable either from terrestrial experiments, or through observations of the motion of solar system bodies. A lower bound for the only parameter used in this extension is set.