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Published in

American Astronomical Society, Astrophysical Journal, 2(718), p. 913-919, 2010

DOI: 10.1088/0004-637x/718/2/913

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Gravitational Lensing Corrections in Flat ΛCDM Cosmology

Journal article published in 2010 by Ronald Kantowski, Bin Chen ORCID, Xinyu Dai ORCID
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

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.