This Thesis presents a new method to simulate and study weak
gravitational lensing of the Cosmic Microwave Background (CMB) and its
correlation with the Large Scale Structure (LSS). We
exploit ray-tracing techniques to follow the photons' path from
the last scattering surface, as they travel throughout a
Universe which is expanding and evolving. The main analysis revolves around
the concept of a light-cone, by compressing the information of
N-Body numerical simulations into a set of lensing planes, which
deflect the light as predicted by (weak) gravitational lensing. We
perform several different numerical tests in order to establish the accuracy
of our reconstruction and the precision of our simulations up to the
arc-minute scale, as we explore these effects by the means of the
two-points statistics.
The main goal is to model non-linear effects of weak lensing by going beyond the
first-order result of the Born approximation. We compare our simulations
with analytical and semi-analytical predictions, as we study the
signal behaviour at different scales and regimes. We confirm the
validity of first order approach up to very small scales ($\ell
\approx 4000$ with the current simulation's set-up, corresponding to few arc-minutes on the sky),
when we find some tension especially with the signal
predicted by high-order perturbation theory in the power
spectrum. Finally, we implement a methodology for creating mock
catalogues of galaxies populating N-Body simulations, in order to apply our
pipeline to model the cross-correlation between large scale
structure traces such as CMB lensing and galaxy catalogues. We show how the
simulated signal can be recovered and compared with theoretical
expectations and observations, enabling a thorough investigation
of structure formation over cosmic time and allowing for a better
understanding of cosmology and astrophysics.
The resulting, end-to-end pipeline going from simulated CMB and LSS,
through lensing and cross correlation of the distorted anisotropies and
the lenses themselves as traced by galaxies, is part of the suites of
codes and validation infrastructure
while approaching high resolution and sensitivity for CMB and LSS
observations, such as the Euclid satellite, or the POLARBEAR ground experiment.
