Forecasts for Low Spin Black Hole Spectroscopy in Horndeski Gravity

We investigate the prospect of using black hole spectroscopy to constrain the parameters of Horndeski gravity through observations of gravitational waves from perturbed black holes. We study the gravitational waves emitted during ringdown from black holes without hair in Horndeski gravity, demonstrating the qualitative differences between such emission in General Relativity and Horndeski theory. In particular, Quasi-Normal Mode frequencies associated with the scalar field spectrum can appear in the emitted gravitational radiation. Analytic expressions for error estimates for both the black hole and Horndeski parameters are calculated using a Fisher Matrix approach, with constraints on the `effective mass' of the Horndeski scalar field of order $\sim 10^{-17}$eV$c^{-2}$ or tighter being shown to be achievable in some scenarios. Estimates for the minimum signal-noise-ratio required to observe such a signal are also presented.