N-body lensed CMB maps: lensing extraction and characterization
  We reconstruct shear maps and angular power spectra from simulated weakly
lensed total intensity (TT) and polarised (EB) maps of the Cosmic Microwave
Background (CMB) anisotropies, obtained using Born approximated ray-tracing
through the N-body simulated Cold Dark Matter (CDM) structures in the
Millennium Simulations (MS). We compare the recovered signal with the
$\Lambda$CDM prediction, on the whole interval of angular scales which is
allowed by the finite box size, extending from the degree scale to the
arcminute, by applying a quadratic estimator in the flat sky limit; we consider
PRISM-like instrumental specification for future generation CMB satellites,
corresponding to arcminute angular resolution of 3.2' and sensitivity of 2.43
${\mu}$K-arcmin. -arcmin. The noise bias in the simulations closely follows the
estimator prediction, becoming dominated by limits in the angular resolution
for the EB signal, at l${\simeq}$1500. The de-biased signal shows no visible
departure from predictions of the weak lensing power within uncertainties, when
considering TT and EB data singularly. In particular, the reconstruction
precision reaches the level of a few percent in bins with $\Delta$l
${\simeq}$100 in the angular multiple interval 1000<l<2000 for TT, and about
10$%$ for EB. Within the adopted specifications, polarisation data do represent
a significant contribution to the lensing shear, which appear to faithfully
trace the underlying N-body structure down to the smallest angular scales
achievable with the present setup, validating at the same time the latter with
respect to semi-analytical predictions from ${\Lambda}$CDM cosmology at the
level of CMB lensing statistics. This work demonstrates the feasibility of CMB
lensing studies based on large scale simulations of cosmological structure
formation in the context of the current and future high resolution and
sensitivity CMB experiment.
