  Scalar fields coupled to gravity through the Ricci scalar have been
considered both as dark matter candidates and as a possible modified gravity
explanation for galactic dynamics. It has recently been demonstrated that the
dynamics of baryonic matter in disk galaxies may be explained, in the absence
of particle dark matter, by a symmetron scalar field that mediates a fifth
force. The symmetron provides a concrete and archetypal field theory within
which to explore how large a role modifications of gravity can play on galactic
scales. In this article, we extend these previous works by asking whether the
same symmetron field can explain the difference between the baryonic and lens
masses of galaxies through a modification of gravity. We consider the
possibilities for minimal modifications of the model and find that this
difference cannot be explained entirely by the symmetron fifth force without
extending the field content of the model. Instead, we are pushed towards a
regime of parameter space where one scalar field both mediates a fifth force
and stores enough energy density that it also contributes to the galaxy's
gravitational potential as a dark matter component, a regime which remains to
be fully explored.
