Test of conformal theory of gravity as an alternative paradigm to dark matter hypothesis from gravitational lensing studies

Weyl's conformal gravity theory, which is considered as a compelling alternative to general relativity theory, has been claimed to describe the observed flat rotation curve feature of spiral galaxies without the need of invoking dark matter. However, it is important to examine whether the Weyl theory can also explain the relevant gravitational lensing observations correctly without considering any dark matter. In this regard, the gravitational bending angle in static spherically space-time (Mannheim-Kazanas metric) in Weyl theory has been calculated by several authors over the last two decades, but the results are found largely divergent. In this work, we have revisited the problem and obtain the correct and consistent expression of the deflection angle in conformal gravity. Subsequently we perform the gravitational lensing analysis. We compare the prediction of Weyl gravity with the gravitational lensing observations of the rich galaxy clusters Abell 370 and Abell 2390 and is found that Weyl theory cannot describe the stated lensing observations without considering dark matter.