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

We use the large cosmological Millennium Simulation (MS) to construct the first all-sky maps of the lensing potential and the angle, aiming at gravitational lensing of the cosmic microwave background (CMB), with the goal of properly including small-scale non-linearities and non-Gaussianity. Exploiting the Born approximation, we implement a map-making procedure based on direct ray tracing through the gravitational potential of the MS. We stack the simulation box in redshift shells up to z ~ 11, producing continuous all-sky maps with arcmin angular resolution. A randomization scheme avoids the repetition of structures along the line of sight, and structures larger than the MS box size are added to supply the missing contribution of large-scale (LS) structures to the lensing signal. The angular power spectra of the projected lensing potential and the deflection-angle modulus agree quite well with semi-analytic estimates on scales down to a few arcmin, while we find a slight excess of power on small scales, which we interpret as being due to non-linear clustering in the MS. Our map-making procedure, combined with the LS adding technique, is ideally suited for studying lensing of CMB anisotropies, for analysing cross-correlations with foreground structures, or other secondary CMB anisotropies such as the Rees-Sciama effect.