Dark energy and extending the geodesic equations of motion: A spectrum of galactic rotation curv

A recently proposed extension of the geodesic equations of motion, where the worldlinetraced by a test particle now depends on the scalar curvature, is used to study theformation of galaxies and galactic rotation curves. This extension is applied to themotion of a fluid in a spherical geometry, resulting in a set of evolution equations forthe fluid in the nonrelativistic and weak gravity limits. Focusing on the stationary solutionsof these equations and choosing a specific class of angular momenta for the fluidin this limit, we show that dynamics under this extension can result in the formation ofgalaxies with rotational velocity curves (RVC) that are consistent with the UniversalRotation Curve (URC), and through previous work on the URC, the observed rotationalvelocity profiles of 1100 spiral galaxies. In particular, a spectrum of RVCs canform under this extension, and we find that the two extreme velocity curves predictedby it brackets the ensemble of URCs constructed from these 1100 velocity profiles.We also find that the asymptotic behavior of the URC is consistent with that of themost probable asymptotic behavior of the RVCs predicted by the extension. A stabilityanalysis of these stationary solutions is also done, and we find them to be stable in thegalactic disk, while in the galactic hub they are stable if the period of oscillations ofperturbations is longer than 0.91+/- 0.31 to 1.58+/- 0.46 billion years