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

Weyl's conformal gravity theory, which is considered as a compelling alternative togeneral relativity theory, has been claimed to describe the observed flat rotation curve featureof spiral galaxies without the need of invoking dark matter. However, it is important to examinewhether the Weyl theory can also explain the relevant gravitational lensing observations correctlywithout considering any dark matter. In this regard, the gravitational bending angle in staticspherically space-time (Mannheim-Kazanas metric) in Weyl theory has been calculated by severalauthors over the last two decades, but the results are found largely divergent. In this work, wehave revisited the problem and obtain the correct and consistent expression of the deflectionangle in conformal gravity. Subsequently we perform the gravitational lensing analysis. We comparethe prediction of Weyl gravity with the gravitational lensing observations of the rich galaxyclusters Abell 370 and Abell 2390 and is found that Weyl theory cannot describe the stated lensingobservations without considering dark matter.