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

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

Automated summary

In this study, the authors investigate the particle content of higher derivative theories of gravity constructed with contractions of the Riemann tensor and its covariant derivatives. It is found that theories involving covariant derivatives of the Riemann tensor may exhibit ghost particles in their spectrum. This could be an indication of non-locality in any healthy UV completion of General Relativity.