Linear Stability Analysis of Dynamical Quadratic Gravity

Abstract

We perform a linear stability analysis of dynamical, quadratic gravity in the high-frequency, geometric optics approximation. This analysis is based on a study of gravitational and scalar modes propagating on spherically-symmetric and axially-symmetric, vacuum solutions of the theory. We find dispersion relations that do no lead to exponential growth of the propagating modes, suggesting the theory is linearly stable on these backgrounds. The modes are found to propagate at subluminal and superluminal speeds, depending on the propagating modes' direction relative to the background geometry, just as in dynamical Chern-Simons gravity.