Unifying static analysis of gravitational structures with a
  scale-dependent scalar field gravity as an alternative to dark matter
  Aims. We investigated the gravitational effects of a scalar field within
scalar-tensor gravity as an alternative to dark matter. Motivated by chameleon,
symmetron and f(R)-gravity models, we studied a phenomenological scenario where
the scalar field has both a mass (i.e. interaction length) and a coupling
constant to the ordinary matter which scale with the local properties of the
considered astrophysical system. Methods. We analysed the feasibility of this
scenario using the modified gravitational potential obtained in its context and
applied it to the galactic and hot gas/stellar dynamics in galaxy clusters and
elliptical/spiral galaxies respectively. This is intended to be a first step in
assessing the viability of this new approach in the context of "alternative
gravity" models. Results. The main results are: 1. the velocity dispersion of
elliptical galaxies can be fitted remarkably well by the suggested scalar
field, with model significance similar to a classical Navarro-Frenk-White dark
halo profile; 2. the analysis of the stellar dynamics and the gas equilibrium
in elliptical galaxies has shown that the scalar field can couple with ordinary
matter with different strengths (different coupling constants) producing and/or
depending on the different clustering state of matter components; 3. elliptical
and spiral galaxies, combined with clusters of galaxies, show evident
correlations among theory parameters which suggest the general validity of our
results at all scales and a way toward a possible unification of the theory for
all types of gravitational systems we considered. All these results demonstrate
that the proposed scalar field scenario can work fairly well as an alternative
to dark matter.
