Gravitational Lensing Corrections in Flat ΛCDM Cosmology

We compute the deflection angle for a light ray traveling in a flat ΛCDM cosmology which encounters a completely condensed mass region to second order inm/r0 and first order inm/r0×Λr 2 0.We find that the most significant correction to the Einstein angle occurs not because of the non-linear terms but instead because the condensed mass is embedded in an expanding cosmology. We predict a decrease in the deflection angle of ∼ 2% for weakly lensed galaxies behind the rich cluster A1689, and that the reduction can be as large as ∼ 5% for similar rich clusters at z ≈ 1. Weak lensing deflection angles caused by galaxies can likewise be reduced by as much as ∼4%. We show that the lowest order correction in which Λ appears is proportional to m/r0 × √ Λr 0 and could cause as much as a ∼0.02% increase in the deflection angle for light that passes through a rich cluster. The lowest order non-linear correction in the mass is proportional to m/r0 × √ m/r0 and can increase the deflection angle by ∼ 0.005% for weak lensing by galaxies. Subject headings: gravitational lensing — cosmology: theory