Are there Einsteinian gravities involving covariant derivatives of the Riemann tensor?

A bstract We study the particle content of higher derivative theories gravity built with contractions Riemann tensor and its covariant derivatives. In absence latter, there is a family exhibiting an Einsteinian spectrum known as generalized quasi-topological gravities. turn, we present no-go result for construction gravities involving derivatives tensor. find evidences suggesting that (truncated series) finite order Lagrangians generically ghosts in their spectrum. This might be interpreted hint non-locality any healthy UV completion General Relativity.