Anisotropic stress as a signature of nonstandard propagation of gravitational waves

We make precise the heretofore ambiguous statement that anisotropic stress is a sign of a modification of gravity. We show that in cosmological solutions of very general classes of models extending gravity - all scalar-tensor theories (Horndeski), Einstein-aether models, and bimetric massive gravity - a direct correspondence exists between perfect fluids apparently carrying anisotropic stress and a modification in the propagation of gravitational waves. Since the anisotropic stress can be measured in a model-independent manner, a comparison of the behavior of gravitational waves from cosmological sources with large-scale-structure formation could, in principle, lead to new constraints on the theory of gravity.