Impact of a global quadratic potential on galactic rotation curves

Abstract

We have made a conformal gravity fit to an available sample of 110 spiral galaxies, and report here on the 20 of those galaxies whose rotation curve data points extend the furthest from galactic centers. We identify the impact on the 20 galaxy data set of a universal de Sitter-like potential term $V(r)=-κc^2r^2/2$ that is induced by inhomogeneities in the cosmic background. This quadratic term accompanies a universal linear potential term $V(r)=γ_0c^2r/2$ that is associated with the cosmic background itself. We find that when these two potential terms are taken in conjunction with the contribution generated by the local luminous matter within the galaxies, the conformal theory is able to account for the rotation curve systematics that is observed in the entire 110 galaxy sample, without the need for any dark matter whatsoever. With the two universal coefficients being found to be of global magnitude, viz. $κ=9.54\times 10^{-54} {\rm cm}^{-2}$ and $γ_0=3.06\times 10^{-30}{\rm cm}^{-1}$, our study suggests that invoking the presence of dark matter may be nothing more than an attempt to describe global effects in purely local galactic terms. With the quadratic potential term having negative sign, galaxies are only able to support bound orbits up to distances of order $γ_0/κ= 3.21\times 10^{23} {\rm cm}$, with global physics thus imposing a natural limit on the size of galaxies.