Born-corrections to weak lensing of the cosmic microwave background temperature and polarisation anisotropies

Abstract: Many weak lensing calculations make use of the Born approximation where the light ray is approximated by a straight path. We examine the effect of Born-corrections for lensing of the cosmic microwave background in an analytical approach by taking perturbative corrections to the geodesic into account. The resulting extra power in the lensing potential spectrum is comparable to the power generated by nonlinear structure formation and affects especially the polarisation spectra, leading to relative changes of the order of one per cent for the $E$-mode spectrum and up to 10 per cent on all scales to the $B$-mode spectrum. In contrast, there is only little change of spectra involving the CMB temperature. Additionally, the corrections excite one more degree of freedom resulting in a deflection component which can not be described as a gradient of the lensing potential as it is related to image rotation in lens-lens coupling. We estimate the magnitude of this effect on the CMB-spectra and find it to be negligible.