GRAVITATIONAL LENSING CORRECTIONS IN FLAT ΛCDM COSMOLOGY

We compute the deflection angle to order (m/r(0))(2) and m/r(0) x Lambda r(0)(2) for a light ray traveling in a flat Lambda CDM cosmology that encounters a completely condensed mass region. We use a Swiss cheese model for the inhomogeneities and find that the most significant correction to the Einstein angle occurs not because of the nonlinear terms but instead occurs because the condensed mass is embedded in a background cosmology. The Swiss cheese model predicts a decrease in the deflection angle of similar to 2% for weakly lensed galaxies behind the rich cluster A1689 and that the reduction can be as large as similar to 5% for similar rich clusters at z approximate to 1. Weak-lensing deflection angles caused by galaxies can likewise be reduced by as much as similar to 4%. We show that the lowest order correction in which Lambda appears is proportional to m/r(0) x root Lambda r(0)(2) and could cause as much as a similar to 0.02% increase in the deflection angle for light that passes through a rich cluster. The lowest order nonlinear correction in the mass is proportional to m/r(0) x root m/r(0) and can increase the deflection angle by similar to 0.005% for weak lensing by galaxies.