Conformal gravity is a higher derivative gravitational theory, with its characteristic feature being, in addition to diffeomorphism invariance, invariance under conformal transformations. In partic-ular, the conformal gravity Lagrangian contains up to 4 th order derivatives of the metric and in 4 spacetime dimensions the action is invariant under local conformal rescalings of the metric tensor. Like most higher derivative gravitational theories, it seems to have a better behavior than General Relativity in the quantum regime, but additionally, it suffers from the problem of ghosts. The theory has been considered in several aspects in the literature, such as in the content of quantum gravity and phenomenology. Furthermore, conformal gravity has been widely studied in the holographic framework.
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