Instabilities of Spherical Solutions with Multiple Galileons and SO(N) Symmetry

TL;DR

This paper investigates the stability and physical properties of spherically symmetric solutions in multi-Galileon theories with SO(N) symmetry, revealing instabilities and superluminal propagation that challenge their viability.

Contribution

It analyzes the existence and stability of spherical solutions in multi-Galileon models with SO(N) symmetry, highlighting the need for more general couplings for consistent theories.

Findings

Spherically symmetric solutions exist with Vainshtein screening.

Gradient instabilities are unavoidable with simple couplings.

Superluminal fluctuations occur around these solutions.

Abstract

The 4-dimensional effective theory arising from an induced gravity action for a co-dimension greater than one brane consists of multiple galileon fields pi^I, I=1...N, invariant under separate Galilean transformations for each scalar, and under an internal SO(N) symmetry. We study the viability of such models by examining spherically symmetric solutions. We find that for general, non-derivative couplings to matter invariant under the internal symmetry, such solutions exist and exhibit a Vainshtein screening effect. By studying perturbations about such solutions, we find both an inevitable gradient instability and fluctuations propagating at superluminal speeds. These findings suggest that more general, derivative couplings to matter are required for the viability of SO(N) galileon theories.