Is negative kinetic energy meta-stable?

TL;DR

This paper investigates whether theories with negative kinetic energy, or ghosts, can be meta-stable over cosmological timescales, analyzing classical, quantum, and field theory behaviors and their stability implications.

Contribution

It demonstrates that ghosts can be meta-stable due to classical lockdown effects and provides analytical and numerical estimates of their run-away rates, especially in gravitational contexts.

Findings

Ghosts undergo classical lockdown if weakly-coupled and non-resonant.

Run-away rates are cosmologically slow in 4-derivative gravity.

Quantum ghost run-away rate is naively infinite in perturbation theory.

Abstract

We explore the possibility that theories with negative kinetic energy (ghosts) can be meta-stable up to cosmologically long times. In classical mechanics, ghosts undergo spontaneous lockdown rather than run-away if weakly-coupled and non-resonant. Physical examples of this phenomenon are shown. In quantum mechanics this leads to meta-stability similar to vacuum decay. In classical field theory, lockdown is broken by resonances and ghosts behave statistically, drifting towards infinite entropy as no thermal equilibrium exists. We analytically and numerically compute the run-away rate finding that it is cosmologically slow in 4-derivative gravity, where ghosts have gravitational interactions only. In quantum field theory the ghost run-away rate is naively infinite in perturbation theory, analogously to what found in early attempts to compute vacuum tunnelling; we do not know the true rate.