The $\Lambda_2$ limit of massive gravity

Abstract

Lorentz-invariant massive gravity is usually associated with a strong coupling scale $\Lambda_3$. By including non-trivial effects from the Stueckelberg modes, we show that about these vacua, one can push the strong coupling scale to higher values and evade the linear vDVZ-discontinuity. For generic parameters of the theory and generic vacua for the Stueckelberg fields, the $\Lambda_2$-decoupling limit of the theory is well-behaved and free of any ghost or gradient-like instabilities. We also discuss the implications for nonlinear sigma models with Lorentzian target spaces.