Role of $\Lambda$ in the Cosmological Lens Equation

The cosmological constant $\Lambda$ affects cosmological gravitational lensing. Effects due to $\Lambda$ can be studied in the framework of the Schwarzschild–de Sitter spacetime. Two novel contributions, which cannot be accounted for by a proper use of angular diameter distances, are derived. First, a term $\delta {\widehat{\alpha }}_{\Lambda }=2mb\Lambda /3$ has to be added to the bending angle, where $m$ is the lens mass and $b$ the impact parameter. Second, $\Lambda$ brings about a difference in the redshifts of multiple images. Both effects are quite small for real astrophysical systems, $\delta {\widehat{\alpha }}_{\Lambda }\lesssim 1\mu \mathrm{arcsec}$ and $\Delta z_s\lesssim {10}^{-7}$.