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(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 vertical bar alpha(B)vertical bar greater than or similar to 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 vertical bar alpha(H)vertical bar greater than or similar to 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.