Massive gravity, the elasticity of space-time and perturbations in the dark sector

Understand

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.