Weak lensing peak count as a probe of f(R) theories
  Weak gravitational lensing by galaxy clusters on faint higher redshift
galaxies has been traditionally used to study the cluster mass distribution and
as a tool to identify clusters as peaks in the shear maps. However, it becomes
soon clear that peaks statistics can also be used as a way to constrain the
underlying cosmological model due to its dependence on both the cosmic
expansion rate and the growth rate of structures. This feature makes peak
statistics particularly interesting from the point of view of discriminating
between General Relativity and modified gravity. Here we consider a general
class of $f(R)$ theories and compute the observable mass function based on the
aperture mass statistics. We complement our theoretical analysis with a Fisher
matrix forecast of the constraints that an Euclid\,-\,like survey can impose on
the $f(R)$ model parameters. We show that peak statistics alone can in
principle discriminate between General Relativity and $f(R)$ models and
strongly constrain the $f(R)$ parameters that are sensitive to the non-linear
growth of structure. However, further analysis is needed in order to include
possible selection function in the peaks redshift determination.
