Fitting galactic rotation curves with conformal gravity and a global
  quadratic potential
  We apply the conformal gravity theory to a sample of 111 spiral galaxies
whose rotation curve data points extend well beyond the optical disk. With no
free parameters other than galactic mass to light ratios, the theory is able to
account for the systematics that is observed in this entire set of rotation
curves without the need for any dark matter at all. In previous applications of
the theory a central role was played by a universal linear potential term
$V(r)=\gamma_0 c^2r/2$ that is generated through the effect of cosmology on
individual galaxies, with the coefficient $\gamma_0=3.06\times 10^{-30} {\rm
cm}^{-1}$ being of cosmological magnitude. Because the current sample is so big
and encompasses some specific galaxies whose data points go out to quite
substantial distances from galactic centers, we are able to identify an
additional globally induced universal term in the data, a quadratic
$V(r)=-\kappa c^2r^2/2$ term that is induced by inhomogeneities in the cosmic
background. With $\kappa$ being found to be of magnitude $\kappa=9.54\times
10^{-54} {\rm cm}^{-2}$, through study of the motions of particles contained
within galaxies we are thus able to both detect the presence of a global de
Sitter-like component and provide a specific value for its strength. Our study
suggests that invoking dark matter may be nothing more than an attempt to
describe global physics effects such as these in purely local galactic terms.
