Conformal Symmetry in Classical Gravity

Since quantizing general relativity remains as intractable a problem as ever, many researchers now look to alternative theories of gravity. Invariance under conformal transformations of the metric is a strong and possibly natural constraint on such theories, although it is not satisfied by general relativity itself. After reviewing the meaning and consequences of conformal invariance in curved spacetime, two ways of formulating a 4-dimensional conformal gravity theory are discussed and critically examined.