Galactic Rotation Curves from Yang-Mills Gravity

Yang-Mills Gravity (YMG) is a gauge field theory based on the $T_4$ group in flat spacetime. In its macroscopic limit, it modifies the trajectories of classical objects such that it serves as an alternative to General Relativity (GR). Since YMG is relatively new and unknown, a brief review of the general theory is given and a more comprehensive list of references is provided. In the present work, we find that the Schwarzchild-like solution to YMG supports a term like $\alpha r$ with constant $\alpha$. This translates into an $r$-term in the effective gravitational potential of classical objects. We use this modified potential to predict the shape of the rotation curves of spiral galaxies, and then use data from SDSS to constrain $\alpha$, which seems to be a free parameter in YMG.