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.
