Conformal Gravity Redux: Ghost-turned-Tachyon

Understand

We analyze conformal gravity in translationally invariant approximation, where the metric is taken to depend on time but not on spatial coordinates.

• We find that the field mode which in perturbation theory has a ghostlike kinetic term, turns into a tachyon when nonlinear interaction is accounted for.
• The kinetic term and potential for this mode have opposite signs.
• Solutions of nonlinear classical equations of motion develop a singularity in finite time determined by the initial conditions.