Vainshtein mechanism in massive gravity nonlinear sigma models

Understand

We study the stability of the Vainshtein screening solution of the massive/bi-gravity based on the massive nonlinear sigma model as the effective action inside the Vainshtein radius.

• The effective action is obtained by taking the $\Lambda_2$ decoupling limit around a curved spacetime.
• First we derive a general consequence that any Ricci flat Vainshtein screening solution is unstable when we take into account the excitation of the scalar graviton only.
• This instability suggests that the nonlinear excitation of the scalar graviton is not sufficient to obtain a successful Vainshtein screening in massive/bi-gravity.