  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.
