In this paper, we fully investigate cosmological scenarios in which dark<br />
matter is non-minimally coupled to an extra scalar degree of freedom. The<br />
interaction is realized by means of conformal and disformal terms in the<br />
transformed gravitational metric. Considering linear perturbation theory, we<br />
show that the growth rate of dark matter differs from the uncoupled case and<br />
that the well-known Kaiser formula undergoes modification. As a result,<br />
redshift space distortion measurements cease to be a direct probe of the linear<br />
growth rate of total matter, since the distortion factor has an extra,<br />
coupling-dependent term. We study the effect of the coupling in three<br />
cosmological models, two conformally and one disformally coupled, and forecast<br />
the constraints on the coupling, and other cosmological parameters, from future<br />
galaxy surveys.