Probing inflation with cosmic microwave background polarization: the weak lensing effect on the covariance of cosmic microwave background spectra

Cosmic microwave background (CMB) anisotropies are modified by the weak lensing effect of intervening large scale structures on the photon path from the last scattering surface to the observer. This has to be accounted for when observational data from sensitive experiments are used to constrain cosmological models. A common approximation for analysing the CMB angular power spectra is including only the Gaussian part of the lensing correction and ignoring the non-Gaussian terms in the error covariance matrix of the spectra. In order to investigate the validity of this approximation, we computed these non-Gaussian terms by using a perturbative expansion method. We present a graphical method for writing down any N point correlation functions at any order in lensing. We use a pedagogical approach to demonstrate that neglecting non-Gaussian terms is an accurate approximation for all polarizations but B, and it will remain so even for the analysis of very sensitive post-Planck experiments. For the B polarization, non-Gaussian contributions up to order 4 must be taken into account.