Removing spurious degrees of freedom from EFT of gravity

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