Full-sky maps for gravitational lensing of the cosmic microwave background

We have constructed the first all-sky cosmic microwave background (CMB) temperature and polarization lensed maps based on a high-resolution cosmological N-body simulation, the Millennium Simulation (MS). We have exploited the lensing potential map obtained using a previously developed map-making procedure which integrates along the line-of-sight the MS dark matter distribution by stacking and randomizing the simulation boxes up to z = 127, and which semi-analytically supplies the large-scale power in the angular lensing potential that is not correctly sampled by the N-body simulation. The lensed sky has been obtained by properly modifying the latest version of the LensPix code to account for the MS structures. We have also produced all-sky lensed maps of the so-called ψE and ψB potentials, which are directly related to the electric and magnetic types of polarization. The angular power spectra of the simulated lensed temperature and polarization maps agree well with semi-analytic estimates up to l <= 2500, while on smaller scales we find a slight excess of power which we interpret as being due to non-linear clustering in the MS. We also observe how non-linear lensing power in the polarized CMB is transferred to large angular scales by suitably misaligned modes in the CMB and the lensing potential. This work is relevant in view of the future CMB probes, as a way to analyse the lensed sky and disentangle the contribution from primordial gravitational waves.