Vainshtein mechanism in massive gravity nonlinear sigma models

TL;DR

This paper investigates the stability of Vainshtein screening solutions in massive gravity models, finding that scalar and vector graviton excitations do not stabilize the solutions, indicating challenges for successful screening.

Contribution

It demonstrates that scalar graviton excitations lead to instability in Vainshtein solutions and shows that vector graviton excitations do not resolve these instabilities in massive/bi-gravity.

Findings

Ricci flat Vainshtein solutions are unstable with scalar graviton excitation.

Linear vector graviton excitations do not stabilize the solutions.

Solutions exhibit ghost and gradient instabilities regardless of parameters.

Abstract

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. Then to see the role of the excitation of the vector graviton, we study perturbations around the static and spherically symmetric solution obtained in bigravity explicitly. As a result, we find that linear excitations of the vector graviton cannot be helpful and the solution still suffers from a ghost and/or a gradient instability for any parameters of the theory for this background.