A quantum ghost coupled polynomially to a harmonic oscillator has unitary evolution and a stable vacuum because a conserved quantity possesses a positive discrete spectrum.
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Apparent instability of metric perturbations in Newtonian gauge for quadratic gravity inflation is a gauge artefact; gauge-invariant variables and other gauges show stable perturbative behaviour.
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Unitary Time Evolution and Vacuum for a Quantum Stable Ghost
A quantum ghost coupled polynomially to a harmonic oscillator has unitary evolution and a stable vacuum because a conserved quantity possesses a positive discrete spectrum.
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Gauge-independent approach to inflation in quadratic gravity
Apparent instability of metric perturbations in Newtonian gauge for quadratic gravity inflation is a gauge artefact; gauge-invariant variables and other gauges show stable perturbative behaviour.