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Many theories of modified gravity with higher order derivatives are usuallyignored because of serious problems that appear due to an additional ghostdegree of freedom. Most dangerously, it causes an immediate decay of thevacuum. However, breaking Lorentz invariance can cure such abominable behavior.By analyzing a model that describes a massive graviton together with aremaining Boulware-Deser ghost mode we show that even ghostly theories ofmodified gravity can yield models that are viable at both classical and quantumlevels and, therefore, they should not generally be ruled out. Furthermore, weidentify the most dangerous quantum scattering process that has the main impacton the decay time and find differences to simple theories that only describe anordinary scalar field and a ghost. Additionally, constraints on the parametersof the theory including some upper bounds on the Lorentz-breaking cutoff scaleare presented. In particular, for a simple theory of massive gravity we findthat a breaking of Lorentz invariance is allowed to happen even at scales abovethe Planck mass. Finally, we discuss the relevance to other theories ofmodified gravity.

A spectre is haunting the cosmos: Quantum stability of massive gravity with ghosts