Removing spurious degrees of freedom from EFT of gravity

In the effective field theory approach to gravity, the Lagrangian density for general relativity is supplemented by generally covariant terms of higher order in the Riemann tensor and its derivatives. At face value, these terms will result in higher derivative equations of motion and additional degrees of freedom beyond those of general relativity. This is seemingly at odds with the goal of effective field theory which is to encode ultraviolet corrections in terms of existing low energy degrees of freedom. Here we apply an action-based procedure for the removal of spurious degrees of freedom for the case of general relativity supplemented by a term cubic in the Riemann tensor. To the order we work in, the resulting reduced theory takes the form of minimally modified gravity, which is a class of modified gravity theories that propagate just the massless spin-2 graviton, but exhibit a preferred frame at short distances due to a deformation of time diffeomorphisms. Our work suggests that this class of theories can be understood as an effective theory of gravity, capturing effects of unknown ultraviolet physics.