Nonlinear Properties of Vielbein Massive Gravity

We consider a special theory of massive gravity, which is obtained in a decoupling limit from a bi– gravity theory in the vielbein formulation, with only cosmological constant-like interactions between the two gravitational sectors. We investigate this theory using the Stückelberg method, and construct a ’t Hooft–Feynman gauge fixing in which the tensor, vector and scalar Stückelberg fields are decoupled. We prove that this model has the softest possible ultraviolet behavior which can be expected from any generic (Lorentz invariant) theory of massive gravity, namely that it becomes strong only at the scale Λ3 = (m 2 gMP ) 1/3 . Finally, we confirm that also this model is plagued by a ghost instability, which, in the Stückelberg formalism, arises from quartic scalar–vector and scalar–tensor interactions. 1 E-mail: [email protected] 2 E-mail: [email protected] 3 E-mail: [email protected]