Local minima of the potential can be metastable up to cosmologically long times thanks to energy conservation. We explore the possibility that theories with negative kinetic energy (ghosts) can be metastable up to cosmologically long times. In classical mechanics, ghosts undergo spontaneous lockdown rather than run away if weakly coupled and nonresonant. Physical examples of this phenomenon are shown. In quantum mechanics, this leads to metastability similar to vacuum decay. In classical field theory, lockdown is broken by resonances and ghosts behave statistically, drifting toward infinite entropy as no thermal equilibrium exists. We analytically and numerically compute the runaway rate finding that it is cosmologically slow in four-derivative gravity, where ghosts have gravitational interactions only. In quantum field theory, the ghost runaway rate is naively infinite in perturbation theory, analogously to what is found in early attempts to compute vacuum tunnelling; we do not know the true rate.

• Received 10 November 2020
• Accepted 3 June 2021

DOI:https://doi.org/10.1103/PhysRevD.103.115025

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Published by the American Physical Society