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 ${\displaystyle g_{ab}\rightarrow \Omega ^{2}(x)g_{ab}}$ where ${\displaystyle g_{ab}}$ is the metric tensor and ${\displaystyle \Omega (x)}$ is a function on spacetime.