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

TL;DR

The paper analyzes the viability of $SO(N)$-invariant multi-galileon theories arising from brane-world scenarios by studying spherically symmetric solutions with a non-derivative, $SO(N)$-invariant matter coupling. It shows that such solutions exist and exhibit Vainshtein screening, with the background aligning along a single field direction $\pi^1$, $\pi^{I\neq1}=0$, but perturbations reveal a gradient instability in the angular sector for the $I=1$ mode and ubiquitous superluminal radial propagation for all modes. These pathologies imply that non-derivative couplings are insufficient for phenomenological viability, motivating derivative couplings like $\partial_\mu\pi^I\partial_\nu\pi_I T^{\mu\nu}$ and/or explicit breaking of $SO(N)$ symmetry (e.g., cascading gravity) to achieve a healthy theory. The work also highlights strong solar-system constraints that further restrict the parameter space, guiding future model-building in higher-codimension galileon theories.

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.

Figures (1)

• Figure 1: Schematic sketch of the solution for $\pi(r)$.