Vacuum instability in Chern-Simons gravity

We explore perturbations about a Friedmann-Robertson-Walker background with a nonvanishing cosmological Chern-Simons scalar field in Chern-Simons gravity. At large momenta one of the two circularly polarized tensor modes becomes ghostlike. We argue that nevertheless the theory does not exhibit classical runaway solutions, except possibly in the relativistic nonlinear regime. However, the ghost modes cause the vacuum state to be quantum mechanically unstable, with a decay rate that is naively infinite. The decay rate can be made finite only if one interprets the theory as an effective quantum field theory valid up to some momentum cutoff $\Lambda$, which violates Lorentz invariance. By demanding that the energy density in photons created by vacuum decay over the lifetime of the Universe not violate observational bounds, we derive strong constraints on the two dimensional parameter space of the theory, consisting of the cutoff $\Lambda$ and the Chern-Simons mass.

Figure 1

Spontaneous production of photons and ghost gravitons from vacuum.

Figure 2

Effective field theory parameter space consisting of the cutoff scale $\Lambda$ and the Chern-Simons mass $m_{\mathrm{cs}}$, in eV. The lightly shaded region is excluded from binary pulsar observations [7], and the darkly shaded region is excluded by consideration of vacuum decay.