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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 worldline

traced by a test particle now depends on the scalar curvature, is used to study the

formation of galaxies and galactic rotation curves. This extension is applied to the

motion of a fluid in a spherical geometry, resulting in a set of evolution equations for

the fluid in the nonrelativistic and weak gravity limits. Focusing on the stationary solutions

of these equations and choosing a specific class of angular momenta for the fluid

in this limit, we show that dynamics under this extension can result in the formation of

galaxies with rotational velocity curves (RVC) that are consistent with the Universal

Rotation Curve (URC), and through previous work on the URC, the observed rotational

velocity profiles of 1100 spiral galaxies. In particular, a spectrum of RVCs can

form under this extension, and we find that the two extreme velocity curves predicted

by 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 the

most probable asymptotic behavior of the RVCs predicted by the extension. A stability

analysis of these stationary solutions is also done, and we find them to be stable in the

galactic disk, while in the galactic hub they are stable if the period of oscillations of

perturbations is longer than 0.91+/- 0.31 to 1.58+/- 0.46 billion years.

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