Gravitational wave interactions in $Λ_3$ models of dark energy

Abstract: We argue that cubic order interactions between two scalar gravitons and one tensor graviton are ubiquitous in models of dark energy where the strong coupling scale is $\Lambda_3$. These interactions can potentially provide efficient decay channels for gravitational waves. They can also lead to gradient instabilities of the scalar perturbations in the presence of large amplitude gravitational waves, e.g. those detected by LIGO/Virgo. In contrast with models in scalar-tensor theories, there is an infinite number of higher order interactions in generic $\Lambda_3$ models, which make it difficult to predict the fate of these instabilities inferred from cubic order interactions.