Large- and intermediate-scale anisotropies of ultra-high-energy cosmic rays

Unveiling the sources of ultra-high-energy cosmic rays remains one of the main challenges in high-energy astrophysics. During their propagation, these charged particles are deflected by extragalactic and Galactic magnetic fields, making it difficult to establish a clear correlation with their potential sources. In this thesis, I investigate large- and intermediate-scale anisotropies in the distribution of ultra-high-energy cosmic-ray arrival directions using a full-sky approach. I apply the harmonic-space cross-correlation power spectrum method to cosmicray data for the first time, showing a promising performance of this method in detecting multipole moments at angular scales smaller than the dipole, offering an improved sensitivity compared to previous studies. I then compare the results of these observations with those from simulations based on theoretical models. In addition, I select the highest-energy events detected by the Pierre Auger Observatory, which are expected to have the highest rigidities and therefore to experience the smallest magnetic deflections, to constrain their possible origins. For this purpose, I develop a backtracking method that accounts for various sources of uncertainty and enables the reconstruction of ultra-high-energy cosmic-ray trajectories through the Galactic magnetic field. This approach is used to test possible correlations between the events and several astrophysical candidates. Overall, these results provide new constraints on the origin of ultra-high-energy cosmic rays and contribute to the ongoing effort to uncover the sources capable accelerating particles to such extreme energies