Weak gravitational lensing by compact objects in fourth order gravity
  We discuss weak lensing characteristics in the gravitational field of a
compact object in the low-energy approximation of fourth order f(R) gravity
theory. The particular solution is characterized by a gravitational strength
parameter $\sigma $ and a distance scale $r_{c}$ much larger than the
Schwarzschild radius. Above $r_{c}$ gravity is strengthened and as a
consequence weak lensing features are modified compared to the Schwarzschild
case. We find a critical impact parameter (depending upon $r_{c}$) for which
the behavior of the deflection angle changes. Using the Virbhadra-Ellis lens
equation we improve the computation of the image positions, Einstein ring
radii, magnification factors and the magnification ratio. We demonstrate that
the magnification ratio as function of image separation obeys a power-law
depending on the parameter $\sigma $, with a double degeneracy. No $\sigma \neq
0$ value gives the same power as the one characterizing Schwarzschild black
holes. As the magnification ratio and the image separation are the lensing
quantities most conveniently determined by direct measurements, future lensing
surveys will be able to constrain the parameter $\sigma $ based on this
prediction.
