Probing the dark matter issue in f(R)-gravity via gravitational lensing
  For a general class of analytic f(R)-gravity theories, we discuss the weak
field limit in view of gravitational lensing. Though an additional Yukawa term
in the gravitational potential modifies dynamics with respect to the standard
Newtonian limit of General Relativity, the motion of massless particles results
unaffected thanks to suitable cancellations in the post-Newtonian limit. Thus,
all the lensing observables are equal to the ones known from General
Relativity. Since f(R)-gravity is claimed, among other things, to be a possible
solution to overcome for the need of dark matter in virialized systems, we
discuss the impact of our results on the dynamical and gravitational lensing
analyses. In this framework, dynamics could, in principle, be able to reproduce
the astrophysical observations without recurring to dark matter, but in the
case of gravitational lensing we find that dark matter is an unavoidable
ingredient. Another important implication is that gravitational lensing, in the
post-Newtonian limit, is not able to constrain these extended theories, since
their predictions do not differ from General Relativity.
