  There is a well known degeneracy between the enhancement of the growth of
large-scale structure produced by modified gravity models and the suppression
due to the free-streaming of massive neutrinos at late times. This makes the
matter power-spectrum alone a poor probe to distinguish between modified
gravity and the concordance $\Lambda$CDM model when neutrino masses are not
strongly constrained. In this work, we investigate the potential of using
redshift-space distortions (RSD) to break this degeneracy when the modification
to gravity is scale-dependent in the form of Hu-Sawicki $f(R)$. We find that if
the linear growth rate can be recovered from the RSD signal, the degeneracy can
be broken at the level of the dark matter field. However, this requires
accurate modelling of the non-linearities in the RSD signal, and we here
present an extension of the standard perturbation theory-based model for
non-linear RSD that includes both Hu-Sawicki $f(R)$ modified gravity and
massive neutrinos.
