The $\Lambda_2$ limit of massive gravity

TL;DR

This paper demonstrates that by considering non-trivial Stueckelberg effects, the strong coupling scale of Lorentz-invariant massive gravity can be raised to $ ext{ extLambda}_2$, avoiding instabilities and the vDVZ-discontinuity.

Contribution

It introduces a $ ext{ extLambda}_2$ decoupling limit in massive gravity that is stable and free of ghosts, extending the understanding of strong coupling scales.

Findings

The $ ext{ extLambda}_2$ limit is well-behaved and ghost-free.

Including Stueckelberg effects raises the strong coupling scale.

Implications for nonlinear sigma models with Lorentzian target spaces.

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.