Classical Stability of the Galileon

TL;DR

This paper investigates the classical stability of the Galileon field theories, revealing that only the DGP model guarantees absolute stability for all solutions, while others may be unstable.

Contribution

It introduces the concept of absolute stability for Galileon theories and demonstrates that only the DGP model possesses this property among general solutions.

Findings

DGP model is absolutely stable for all solutions.

Most other Galileon models lack absolute stability.

Unstable solutions could have astrophysical implications.

Abstract

We consider the classical equations of motion for a single Galileon field with generic parameters in the presence of non-relativistic sources. We introduce the concept of absolute stability of a theory: if one can show that a field at a single point---like infinity for instance---in spacetime is stable, then stability of the field over the rest of spacetime is guaranteed for any positive energy source configuration. The Dvali-Gabadadze-Porrati (DGP) model is stable in this manner, and previous studies of spherically symmetric solutions suggest that certain classes of the single field Galileon (of which the DGP model is a subclass) may have this property as well. We find, however, that when general solutions are considered this is not the case. In fact, when considering generic solutions there are no choices of free parameters in the Galileon theory that will lead to absolute stability except the DGP choice. Our analysis indicates that the DGP model is an exceptional choice among the large class of possible single field Galileon theories. This implies that if general solutions (non-spherically symmetric) exist they may be unstable. Given astrophysical motivation for the Galileon, further investigation into these unstable solutions may prove fruitful.