American Astronomical Society, Astrophysical Journal, 2(718), p. 913-919, 2010
DOI: 10.1088/0004-637x/718/2/913
Full text: Download
We compute the deflection angle to order (m/r 0) 2 and m/r 0 × Λr 2 0 for a light ray traveling in a flat ΛCDM cosmology which 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 non-linear 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 ∼ 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/r 0 × Λr 2 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/r 0 × m/r 0 and can increase the deflection angle by ∼ 0.005% for weak lensing by galaxies.