Goldstone models of modified gravity
  We investigate scalar-tensor theories where matter couples to the scalar
field via a kinetically dependent conformal coupling. These models can be seen
as the low-energy description of invariant field theories under a global
Abelian symmetry. The scalar field is then identified with the Goldstone mode
of the broken symmetry. It turns out that the properties of these models are
very similar to the ones of ultralocal theories where the scalar-field value is
directly determined by the local matter density. This leads to a complete
screening of the fifth force in the Solar System and between compact objects,
through the ultralocal screening mechanism. On the other hand, the fifth force
can have large effects in extended structures with large-scale density
gradients, such as galactic halos. Interestingly, it can either amplify or damp
Newtonian gravity, depending on the model parameters. We also study the
background cosmology and the linear cosmological perturbations. The background
cosmology is hardly different from its $\Lambda$-CDM counterpart whilst
cosmological perturbations crucially depend on whether the coupling function is
convex or concave. For concave functions, growth is hindered by the
repulsiveness of the fifth force whilst it is enhanced in the convex case. In
both cases, the departures from the $\Lambda$-CDM cosmology increase on smaller
scales and peak for galactic structures. For concave functions, the formation
of structure is largely altered below some characteristic mass, as smaller
structures are delayed and would form later through fragmentation, as in some
warm dark matter scenarios. For convex models, small structures form more
easily than in the $\Lambda$-CDM scenario.
