Cosmic Microwave Background anomalies: models and interpretation

The current standard cosmological model --the so called LambdaCDM model -- provides an excellent fit to a variety of cosmological data, in primis the temperature anisotropies and polarization of the Cosmic Microwave Background (CMB) radiation. However, as confirmed by the latest Planck satellite data, on the largest angular scales some "anomalies" in the behavior of the CMB fluctuations have been reported. Despite the fact that their statistical significance remains at the 3-sigma level, they have been independently measured previously also by the WAMP satellite, and at the moment a compelling explanation in terms of systematics and or foregrounds does not exist. This might open a window into new physics, probably related to the early Universe, since the largest scales where these anomalies have been reported are the most sensitive to the initial conditions of our universe (e.g. some of these anomalies would hint to a small deviation from statistical isotropy, which is indeed one of the pillars the standard cosmological model is based on). The Thesis aims, first of all, at providing a review of some of the most important large-scale anomalies that have been reported in the CMB data. Then it aims at a detailed study of the various cosmological mechanisms that have been proposed so far to explain such features, especially those related to inflationary models (i.e. to an early epoch of accelerated expansion -- inflation--the universe went through, which gave rise to the first density perturbations, the seeds for the subsequent formation of all the structures we see in the Universe). An original goal of the Thesis work would be in particular to explore possibly new solutions to these puzzles, trying to invoke models of inflation characterized by some amount of primordial non-Gaussianity. Particular attention would be dedicated in this context to the so called stochastic approach to inflation, where the primordial quantum fluctuations of the fields present during the inflationary epoch are studied via stochastic equations of motion.