Kinematic Sunyaev-Zel'dovich effect: non-linear modelling of the velocity field for cosmological and astrophysical applications

The secondary anisotropies of the Cosmic Microwave Background (CMB), which formed after the last scattering, carry a wealth of information of both cosmological and astrophysical interest. This study explores one of them, the kinematic Sunyaev-Zel'dovich (kSZ) effect, resulting from the bulk motion of virialised masses of ionised gas such as galaxy clusters, which leads to a Doppler shift in the CMB temperature. This temperature shift is proportional to the peculiar velocity of the target cluster and most importantly it is independent on redshift, hence unaffected by cosmological dimming. Recent CMB surveys sensitive to the kSZ effect, such as Planck or ACTPol as well as the next generation CMB-S4 experiment, combined with galaxy redshift surveys performed by the more recent or forthcoming instruments such as SDSS-III/BOSS, DESI, PFS, or Euclid-NISP, are yielding a unique and powerful observational tool for measuring large-scale peculiar velocities. This thesis is intended to go beyond the standard modelling of peculiar velocities, which relies on the linear perturbation theory valid on large scales, and explore a non-linear model of peculiar velocities based on the extended-Fast-Action-Minimization (eFAM) method (Sarpa et al. 2019). Appropriate estimators of the kSZ signal are then considered to assess the actual improvement and capability for future cosmological and astrophysical applications.