Light bending by the cosmological constant
  We revisit the question of whether the cosmological constant $\Lambda$
affects the cosmological gravitational bending of light, by numerical
integration of the geodesic equations for a Swiss cheese model consisting of a
point mass and a compensated vacuole, in a Friedmann-Robertson-Walker
background. We find that there is virtually no dependence of the light bending
on the cosmological constant that is not already accounted for in the angular
diameter distances of the standard lensing equations, plus small modifications
that arise because the bending is restricted to a finite region covered by the
hole. The residual $\Lambda$ dependence for a $10^{13}\,M_{\odot}$ lens is at
the level of 1 part in $10^7$, and even this might be accounted for by small
changes in the hole size evolution as the photon crosses. We therefore conclude
that there is no need for modification of the standard cosmological lensing
equations in the presence of a cosmological constant.
