Vacuum Instability in Chern-Simons Gravity

TL;DR

This paper investigates the stability of Chern-Simons gravity, revealing ghost modes that lead to quantum vacuum decay and deriving constraints on the theory's parameters based on observational bounds.

Contribution

It provides a detailed analysis of perturbations in Chern-Simons gravity, identifying ghost modes and their implications for vacuum stability and observational constraints.

Findings

Ghost modes cause quantum vacuum instability.

Vacuum decay rate depends on a Lorentz-violating cutoff.

Constraints on theory parameters ensure consistency with observations.

Abstract

We explore perturbations about a Friedmann-Robertson-Walker background 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, 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 and the Chern-Simons mass.