Ghost-Free Derivative Interactions for a Massive Graviton

If the kinetic interactions of a Lorentz-invariant massive graviton are Einstein-Hilbert, then the only possible potential terms free from the Boulware-Deser ghost are those of de Rham, Gabadadze and Tolley (dRGT). We point out there are other possibilities if the kinetic terms are not required to be Einstein-Hilbert. We construct pseudo-linear ghost-free potentials, terms that derive in a natural way from the linear theory. The simplicity of this approach allows us to construct diffeomorphism non-invariant higher-derivative interaction terms that do not introduce ghosts. We conjecture that these terms should have counterparts in the full dRGT theory. These terms would introduce new free parameters into the theory and may change some of the conclusions heretofore drawn.