Vainshtein mechanism in Gauss-Bonnet gravity and Galileon aether

TL;DR

This paper derives the field equations for 4D Gauss-Bonnet gravity, demonstrating the Vainshtein mechanism's operation, analyzing stability, and exploring superluminal behavior and causal structure in the context of scalar-tensor theories.

Contribution

It provides a detailed derivation of 4D Gauss-Bonnet gravity equations, shows the Vainshtein mechanism's effectiveness, and clarifies stability and superluminal issues in scalar-tensor frameworks.

Findings

Vainshtein mechanism suppresses fifth force inside a sphere.

Superluminal perturbations occur but do not violate causality.

Stability conditions for Friedmann universe are established.

Abstract

We derive field equations of Gauss-Bonnet gravity in 4 dimensions after dimensional reduction of the action and demonstrate that in this scenario Vainshtein mechanism operates in the flat spherically symmetric background. We show that inside this Vainshtein sphere the fifth force is negligibly small compared to the gravitational force. We also investigate stability of the spherically symmetric solution, clarify the vocabulary used in the literature about the hyperbolicity of the equation and the ghost-Laplacian stability conditions. We find superluminal behavior of the perturbation of the field in the radial direction. However, because of the presence of the non linear terms, the structure of the space-time is modified and as a result the field does not propagate in the Minkowski metric but rather in an "aether" composed by the scalar field $\pi(r)$. We thereby demonstrate that the superluminal behavior does not create time paradoxes thank to the absence of Causal Closed Curves. We also derive the stability conditions for Friedmann Universe in context with scalar and tensor perturbations.