Dark Energy and Extending the Geodesic Equations of Motion: A Spectrum of Galactic Rotation Curves

TL;DR

This paper explores how extending the geodesic equations of motion to depend on scalar curvature can produce galaxy rotation curves consistent with observations, offering a potential alternative to dark matter explanations.

Contribution

It introduces a novel extension of geodesic equations that accounts for scalar curvature, leading to realistic galaxy rotation curves matching observational data.

Findings

The extension produces a spectrum of rotation curves consistent with the Universal Rotation Curve.

Predicted velocity curves bracket the observed ensemble of 1100 spiral galaxies.

Stationary solutions are stable in galactic disks and have quantifiable stability periods in the galactic hub.

Abstract

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 the 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 $0.91_{\pm0.31}$ to $1.58_{\pm 0.46}$ billion years.