Dark-Energy Instabilities induced by Gravitational Waves

We point out that dark-energy perturbations may become unstable in the presence of a gravitational wave of sufficiently large amplitude. We study this effect for the cubic Horndeski operator (braiding), proportional to $\alpha_{\rm B}$. The scalar that describes dark-energy fluctuations features ghost and/or gradient instabilities for gravitational-wave amplitudes that are produced by typical binary systems. Taking into account the populations of binary systems, we conclude that the instability is triggered in the whole Universe for $|\alpha_{\rm B} |\gtrsim 10^{-2}$, i.e. when the modification of gravity is sizeable. The instability is triggered by massive black-hole binaries down to frequencies corresponding to $10^{10}$ km: the instability is thus robust, unless new physics enters on even longer wavelengths. The fate of the instability and the subsequent time-evolution of the system depend on the UV completion, so that the theory may end up in a state very different from the original one. The same kind of instability is present in beyond-Horndeski theories for $|\alpha_{\rm H}| \gtrsim 10^{-20}$. In conclusion, the only dark-energy theories with sizeable cosmological effects that avoid these problems are $k$-essence models, with a possible conformal coupling with matter.