Emergence of ghosts in Horndeski theory

Abstract

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). We discuss a relation between the ghost and the appearance of closed causal curves for such solutions.

14 pages, 4 figures; v2: clarifications added, matches published version

References in corpus (5)

• Imperfect Dark Energy from Kinetic Gravity Braiding
• Dark-Energy Instabilities induced by Gravitational Waves
• Caustics for Spherical Waves
• Wave propagation and shock formation in the most general scalar-tensor theories
• Plane waves in the generalized Galileon theory

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