Simulated all-sky maps of the weak gravitational lensing distortion of the CMB

We use the large cosmological Millennium Simulation (MS) to construct the first all-sky maps of the lensing potential and the deflection angle, aiming at gravitational lensing of the CMB. 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 arcminute angular resolution. A randomization scheme avoids repetition of structures along the line of sight. The angular power spectra of the projected lensing potential and the deflection-angle modulus agree well with semi-analytic estimates on scales between a few arcminutes and about one degree. We find a deficit in power on large scales and an excess in the deflection-angle power on small scales, which we interpret as due to non-linear clustering in the MS. Our map-making procedure is ideally suited for studying lensing of CMB anisotropies, for analyzing cross-correlations with foreground structures, or other secondary CMB anisotropies such as the Rees- Sciama effect.