Classical Stability of the Galileon

Understand

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.