A journey through the non-Gaussian universe

Over the past three decades, precise measurements have significantly advanced our understanding of the universe, leading to the establishment of a standard cosmological model, known as the $Lambda$CDM. This model has successfully explained a wide range of observations, including the cosmic microwave background radiation (CMB), the distribution of galaxies, and the accelerated expansion of the universe. Its robustness and consistency with observational data have made it the foundation of modern cosmology. However, there are several aspects of our universe that are unanswered. This dissertation delves into some of the possible extensions of the $Lambda$CDM model and explores ways to refine constraints on fundamental cosmological parameters. The first part of the thesis presents an extensive review on topics of modern cosmology relevant to the thesis, including cosmic inflation, cosmological perturbations and weak gravitational lensing. The second part is dedicated to the original research work performed by the author. In chapter 5, we discuss fundamental limitations on constraining primordial non-Gaussianity and identify promising observables for upcoming CMB and large scale structure experiments. In chapter 6, we build the groundwork for the reconstruction of the CMB lensing convergence bispectrum, studying, for the first time, some of the observational challenges. In chapter 7, we explore the potential of the cross-correlation between radio cosmic shear and CMB lensing in constraining $Lambda$CDM parameters and the neutrino sector