Cosmological Perturbation Theory beyond shell-crossing: Schrödinger equation approach

In this dissertation, in order to study the growth of the density fluctuations of the Cold Dark Matter, the standard perturbation techniques, such as Eulerian perturbation theory and Zel'dovich approximation, have been reviewed. In the second part of our work, we introduce a novel approach to the study of large–scale structure formation in which the Cold Dark Matter is modelled by a complex scalar field whose dynamics are ruled by coupled Schrodinger and Poisson equations. In the last part, we show that results predicted by "tree-level" perturbation theory for the cold dark matter are perfectly recovered.