Emergence of ghosts in Horndeski theory

Understand

We show that starting from initial conditions with stable perturbations, evolution of a galileon scalar field results in the appearance of a ghost later on.

• To demonstrate this, we consider a theory with k-essence and cubic galileon Lagrangians on a fixed Minkowski background.
• Explicit analytical solutions of simple waves are constructed, on top of which a healthy scalar degree of freedom is shown to be converted onto a ghost.
• Such a transformation is smooth and moreover perturbations remain hyperbolic all the time (until a caustic forms).