Energy Density Perturbations in Two-Fileds Inflationary Models

The general problem addressed in this thesis is that of understanding the origin of the primordial inhomogeneities of the energy density which gave rise to the observed large scale structure of the universe. My purpose has been to work out the link between the perturbations arising in different inflationary models and the initial conditions assumed in phenomenological models for structure formation. In particular, I have considered inflationary models when more than one scalar field is present during inflation, and I have studied the possibility that the resulting energy density fluctuations are of the isocurvature type or have a non-Gaussian distribution. In the first part of the thesis some topics relevant for the origin of the structures in the inflationary cosmology are reviewed. In chapter 1, the main tools for the description of the density inhomogeneities are discussed. In particular, the different possible primordial initial conditions on the perturbations are characterized and the possibility that they arise in the frame of inflation is analysed. We also discuss the most usual scenarios for the formation of structure and their viability. Finally, some relevant issues for the evolution of the density perturbations are presented. In chapter 2, the inflationary scenario is reviewed, the motivations for it are presented and the main models proposed in which it can be realised are introduced. We discuss how density fluctuations are originated from quantum fluctuations of the scalar field which drives inflation, and how they evolve from the time when the associated wavelengths leave the Hubble radius during inflation up to when they cross it again in the radiation or matter dominated era. In the last section, we present the stochastic approach to inflation and discuss its advantages and applications. In the last two subsections, a part of some original work in progress in collaboration with M. Mijic about the structure of space-time arising in stochastic inflation is reported. The second part of the thesis contains the bulk of my original contribution which essentially deals with perturbations originated in inflationary models when more than one scalar field is present. In chapter 3 the possibility that the initial conditions required in phenomenological isocurvature models are realised in the different two field models proposed in the literature is analysed. This involves, firstly, the determination of the perturbations in the classical variables, such as the energy density and velocity associated to each field, originated by the quantum fluctuations of both fields. Further, it requires the study of the subsequent evolution of the fluctuations and the comparison with the initial perturbations needed in the phenomenological models during the radiation dominated era, when these initial conditions are generally imposed. We find that the model in which the additional scalar field decays into thermal radiation after baryogenesis, giving rise to fluctuations in the initially smooth entropy per baryon ratio, does not provide these isocurvature initial conditions as was expected. It turns out that in the case in which the second weakly interacting scalar field remains as a dark matter component up to the present epoch, in the case in which axions are considered and in the spontaneous baryogenesis model the isocurvature initial conditions can be originated. In chapter 4 the two-field models are analysed in the stochastic inflation frame. This research has been developed in collaboration with S. Matarrese, A. Ortolan and F. Lucchin. The stochastic approach is first extended to deal with more than one scalar field. The Langevin and Fokker-Planck equations for the joint probability are derived for a general two-field model. We then analyse in detail the case of a massless non-dominating field in a power-law inflation driven by an inflaton with an exponential potential. We study the statistics of the distribution of the non-dominating field. We obtain that in spite of being a free field, it shows highly non- gaussian behaviour on scales much larger than the present horizon; on observable ;cales it gives rise to isocurvature perturbations which are both essentially Gaussian and have a scale invariant spectrum.