The Universe in many nutshells: high resolution simulations of CMB weak gravitational lensing

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.