Journal Article

On the validity of the Born approximation for weak cosmic flexions

Björn Malte Schäfer, Lavinia Heisenberg, Angelos F. Kalovidouris and David J. Bacon

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 420, issue 1, pages 455-467
Published in print February 2012 | ISSN: 0035-8711
Published online January 2012 | e-ISSN: 1365-2966 | DOI:
On the validity of the Born approximation for weak cosmic flexions

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Weak lensing calculations are often made under the assumption of the Born approximation, where the ray path is approximated as a straight radial line. In addition, lens–lens couplings where there are several deflections along the light ray are often neglected. We examine the effect of dropping the Born approximation and taking lens–lens couplings into account, for weak lensing effects up to second order (cosmic flexion), by making a perturbative expansion in the light path. We present a diagrammatic representation of the resulting corrections to the lensing effects. The flexion signal, which measures the derivative of the density field, acquires correction terms proportional to the squared gravitational shear; we also find that by dropping the Born approximation, two further degrees of freedom of the lensing distortion can be excited (the twist components), in addition to the four standard flexion components. We derive angular power spectra of the flexion and twist, with and without the Born approximation and lens–lens couplings and confirm that the Born approximation is an excellent approximation for weak cosmic flexions, but may fail in the strong lensing regime.

Keywords: gravitational lensing: weak; methods: analytical; large-scale structure of Universe

Journal Article.  6929 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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