  We consider a class of modified gravity models where the terms added to the
standard Einstein-Hilbert Lagrangian are just a function of the metric only.
For linearized perturbations around an isotropic space-time, this class of
models is entirely specified by a rank 4 tensor that encodes possibly
time-dependent masses for the gravitons. This tensor has the same symmetries as
an elasticity tensor, suggesting an interpretation of massive gravity as an
effective rigidity of space-time. If we choose a form for this tensor which is
compatible with the symmetries of FRW and enforce full reparameterization
invariance, then the only theory possible is a cosmological constant. However,
in the case where the theory is only time translation invariant, the ghost-free
massive gravity theory is equivalent to the elastic dark energy scenario with
the extra Lorentz violating vector giving rise to 2 transverse and 1
longitudinal degrees of freedom, whereas when one demands spatial translation
invariance one is left with scalar field theory with a non-standard kinetic
term.
