Lensing in the McVittie metric

We investigate the effect of the cosmological expansion on the bending of light due to an isolated pointlike mass. We adopt the McVittie metric as the model for the geometry of the lens. Assuming a constant Hubble factor, we find an analytic expression involving the bending angle, which turns out to be increased by a contribution 1 + z(L), where zL is the redshift of the lens. Employing the lens equation in the thin lens approximation, we find that for Einstein ring systems, the lens mass estimation gains a correction (1 + z(S))/(1 + z(L)) with respect to the one based on the usual formula.