Simulating weak lensing of CMB maps

Aims. Accurate predictions of cosmic microwave background (CMB) anisotropies and polarization are required for analyzing future CMB data sets, which ultimately require accurately simulated lensed maps. Methods. We present a fast, arbitrarily accurate method to simulate the effect of gravitational lensing of the CMB anisotropies and polarization fields by large-scale structures on arbitrarily spaced grid points over a unit sphere using a non-equispaced fast Fourier transform (NFFT). Results. The angular power spectrum of the simulated lensed CMB map, particularly the B-mode of polarization, agrees extremely well with analytical predictions. The analytical derivation of CMB-lensed spectra is based on non-trivial, partially resummed perturbative expansions of the correlation functions, for which our simulations therefore provide an accurate numerical validation. We demonstrate the efficiency and accuracy of the method and exhibit their dependence on the algorithm parameters. Lensed CMB maps simulated in this method are a useful tool for the analysis and interpretation of upcoming CMB experiments, such as PLANCK and ACT. Our code is available on request.