Modified gravity models and the central cusp of dark matter halos in
  galaxies
  The N-body dark matter (DM) simulations point that DM density profiles, e.g.
the NFW halo, should be cuspy in its center, but observations disfavour this
kind of DM profile. Here we consider whether the observed rotation curves
"close" to the galactic centre can favour modified gravity models in comparison
to the NFW halo, and how to quantify such difference. Two explicit modified
gravity models are considered, MOND and a more recent approach called RGGR (in
reference to Renormalization Group effects in General Relativity). It is also
the purpose of this work to significantly extend the sample on which RGGR has
been tested in comparison to other approaches. By analysing 62 galaxies from
five samples, we find that: i) there is a radius, given by half the disk scale
length, below which RGGR and MOND can match the data about as well or better
than NFW, albeit the formers have fewer free parameters; ii) considering the
complete rotation curve data, RGGR could achieve fits with better agreement
than MOND, and almost as good as a NFW halo with two free parameters (NFW and
RGGR have respectively two and one more free parameters than MOND).
