On the validity of the Born approximation for weak cosmic flexions
  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,
except at very small scales.
