Gravitational lensing in fourth order gravity

Abstract

Gravitational lensing is investigated in the weak field limit of fourth order gravity in which the Lagrangian of the gravitational field is modified by replacing the Ricci scalar curvature R with an analytical expression $f(R)$. Considering the case of a pointlike lens, we study the behaviour of the deflection angle in the case of power law Lagrangians, i.e. with f(R) = f_0 R^n. In order to investigate possible detectable signatures, the position of the Einstein ring and the solutions of the lens equation are evaluated considering the change with respect to the standard case. Effects on the amplification of the images and the Paczynski curve in microlensing experiments are also estimated.