(The) classical stability of conformal gravity in the minkowski background

Abstract

It is verified that the conformal gravity with $R^2$ terms is classically unstable in the Minkowski background when the coupling constant c is $-\frac{1}{6}$. In this case, it can be shown that the massless state can be made stable when the parameters introduced in constructing the conformal gravity satisfy some conditions, but the massive states can not be made stable.