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 $V_{\kappa }(r)=-\kappa c^2{r}^2/2$ with $\kappa =9.54\times {10}^{-54}{\mathrm{cm}}^{-2}$ induced by cosmic inhomogeneities. When $V_{\kappa }(r)$ is taken in conjunction with both a universal linear potential $V_{{\gamma }_0}(r)={\gamma }_0{c}^{2}r/2$ with ${\gamma }_0=3.06\times {10}^{-30}{\mathrm{cm}}^{-1}$ 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 $V_{\kappa }(r)$ being negative, galaxies can only support bound orbits up to distances of order ${\gamma }_0/\kappa =100\mathrm{kpc}$, with global physics imposing a limit on the size of galaxies.

• Received 23 November 2010

DOI:https://doi.org/10.1103/PhysRevLett.106.121101