On the validity of the Born approximation for weak cosmic flexions

Authors

  • Björn Malte Schäfer,

    Corresponding author
    1. Institut d’Astrophysique Spatiale, Université de Paris XI, bâtiment 120-121, Centre universitaire d’Orsay, 91400 Orsay CEDEX, France
    2. Astronomisches Recheninstitut, Zentrum für Astronomie, Universität Heidelberg, Mönchhofstraße 12, 69120 Heidelberg, Germany
      E-mail: spirou@ita.uni-heidelberg.de
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  • Lavinia Heisenberg,

    1. Institut für theoretische Astrophysik, Zentrum für Astronomie, Universität Heidelberg, Albert-Ueberle-Straße 2, 69120 Heidelberg, Germany
    2. Université de Genève, Département de Physique Théorique, 24, quai Ernest Ansermet, 1211 Genève, Switzerland
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  • Angelos F. Kalovidouris,

    1. Astronomisches Recheninstitut, Zentrum für Astronomie, Universität Heidelberg, Mönchhofstraße 12, 69120 Heidelberg, Germany
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  • David J. Bacon

    1. Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Burnaby Road, Portsmouth PO1 3FX
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E-mail: spirou@ita.uni-heidelberg.de

ABSTRACT

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.

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