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.
