New Perspectives for the First Second: Preheating of Fermions and Extra-Dimensions

In this thesis I discuss two separate issues related to the very early Universe. The first of them is preheating of fermions. Creation of matter from the inflaton field is one of the most active areas of research of the inflationary scenario. In the last ten years, it has been realized that the first stages of this process are typically governed by relevant nonperturbative production of particles. Creation of bosons is very efficient, since it is characterized by stimulated particle emission into energy bands with large occupation number. It was very recently realized that preheating of fermions can be in some cases even more relevant, despite large occupation numbers are forbidden by Pauli principle. In the first part of the thesis I review the analyses (first numerical and then analytical) which have lead to this conclusion. I then discuss the possible implications for leptogenesis. The second part of the thesis is instead devoted to extra dimensions. The last two and a half years have witnessed a formidable interest in models (I will simply refer to them as to "brane models") where the extra-dimensions manifest themselves not too far from the electroweak scale. The initial motivation for these studies was to provide a solution to the hierarchy problem. I discuss this issue in the first chapter of this part, where brane models are introduced. ·while these scenarios are compatible with the Newton law at the distances we presently probe, they can lead to a very interesting new phenomenology both in accelerator physics and in cosmology. Concerning the latter, I discuss possible modifications of the standard baryogenesis scenarios and of the cosmological evolution of the Universe.