Impact of a Global Quadratic Potential on Galactic Rotation Curves

We present a conformal gravity fit to the 20 largest of a sample of 110 spiral galaxies. We identify the presence of a universal quadratic potential V_κ(r)=-κc²r²/2 with κ=9.54×10^-54cm^-2 induced by cosmic inhomogeneities. When V_κ(r) is taken in conjunction with both a universal linear potential V_γ₀(r)=γ₀c²r/2 with γ₀=3.06×10^-30cm^-1 generated by the homogeneous cosmic background and the contribution generated by the local luminous matter in galaxies, the theory then accounts for the rotation curve systematics observed in the entire 110 galaxies, without the need for any dark matter whatsoever. Our study suggests that using dark matter may be nothing more than an attempt to describe global effects in purely local galactic terms. With V_κ(r) being negative, galaxies can only support bound orbits up to distances of order γ₀/κ=100kpc, with global physics imposing a limit on the size of galaxies.