Quantum description of inflation

In this thesis I want to analyze what happens when an inflationary space-time is studied as a collection of quanta. Classically the inflationary universe can be described by the equation of moto for the metric tensor field and for the inflaton field. My purpose is to deal the two fields as systems of particles, called respectively gravitons and inflatons. Thus, the fundamental quantum quantities that are taken into account to describe these systems, are the particle occupation numbers and the constant couplings between them. Therefore, in addition to the equations of moto for the classical quantities, had to be deduced the temporal evolution for the number of quanta of the two systems. What I will show is that, the equation for the classical and quantum models will give the same interpretation for the space-time, untill the microscopic interactions between quanta become important. The quantum correction that rises, leads to a new interpretation of the inflationary universe. Briefly, in the inflaton model exists a limit in wich can be recovered the well know de Sitter metric, instead this is not more true when the quantum interactions between quanta of the classical fields are are taken into account.\\ Before analyzing the quantum model of inflation, I will show in the second chapter, the corpuscolar interpretation of the black hole. Indeed, it constitutes an instructive model in wich is present only the gravitational field, and the dynamics of the quanta associated, is very similar to that of the inflationary model. The reason can be searched in the statistichal features of the respectively systems. In both models, I will prove that they are Bose-Einstein condensates, constitued by many very weakly interagent quanta, at critical phase point.\\ To conclude, in the last chapter I will show an alternative theory of gravity that inside itself, encodes the inflationary universe, and I will try to quantizy it.