What is Conformal gravity?

Conformal gravity refers to gravity theories that are invariant under conformal transformations in the Riemannian geometry sense; more accurately, they are invariant under Weyl transformations g a b → Ω 2 g a b {\displaystyle g_{ab}\rightarrow \Omega ^{2}g_{ab}} where g a b {\displaystyle g_{ab}} is the metric tensor and Ω {\displaystyle \Omega } is a function on spacetime.