  Modifications of General Relativity generically contain additional degrees of
freedom that can mediate forces between matter particles. One of the common
manifestations of a fifth force in alternative gravity theories is a difference
between the gravitational potentials felt by relativistic and non-relativistic
particles, also known as "the gravitational slip". In contrast, a fifth force
between dark matter particles, due to dark sector interaction, does not cause a
gravitational slip, making the latter a possible smoking gun of modified
gravity. In this article, we point out that a force acting on dark matter
particles, as in models of coupled quintessence, would also manifest itself as
a measurement of an effective gravitational slip by cosmological surveys of
large-scale structure. This is linked to the fact that redshift-space
distortions due to peculiar motion of galaxies do not provide a measurement of
the true gravitational potential if dark matter is affected by a fifth force.
Hence, it is extremely challenging to distinguish a dark sector interaction
from a modification of gravity with cosmological data alone. Future
observations of gravitational redshift from galaxy surveys can help to break
the degeneracy between these possibilities, by providing a direct measurement
of the distortion of time. We discuss this and other possible ways to resolve
this important question.
