Low energy ghosts and the Jeans’ instability

We show that a massless canonical scalar field minimally coupled to general relativity can become a tachyonic ghost at low energies around a background in which the scalar's gradient is spacelike. By performing a canonical transformation we demonstrate that this low energy ghost can be recast, at the level of the action, in a form of a fluid that undergoes a Jeans-like instability affecting only modes with large wavelength. This illustrates that low energy tachyonic ghosts do not lead to a catastrophic quantum vacuum instability, unlike the usual high-energy ghost degrees of freedom.