Strong lensing as a test for Conformal Weyl Gravity

Conformal Weyl Gravity (CWG) predicts galactic rotation curves without invoking dark matter. This makes CWG an interesting candidate theory as an alternative to GR. This removal of the necessity of dark matter arises because the exact exterior solution in CWG for a static, spherically symmetric source provides a linear potential $\gamma r$, which can explain the observed galactic rotation curves with a value for $\gamma$ given by $\sim + 10^{-26} \mathrm{m}^{-1}$. Previous work has also shown that CWG can explain lensing observations, but with $\gamma\sim - 10^{-26} \mathrm{m}^{-1}$ in order to ensure converging rays of light rather than diverging ones. Even though different expressions for the angle of deflection have been derived in CWG in order to remove this inconsistency, this paper shows that the $\gamma$ required to fit the lensing data is several orders of magnitude higher than that required to fit the galactic rotation curves.