  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.
