Abstract : The high accuracy in the measurements of the cosmic microwave background requires to understand in details the underlying physics in order to draw relevant conclusions for the primordial phase of the universe. In this thesis, we study the theory of non-linear perturbations in the framework of general relativity. Our goal is to determine the transfer of the metric perturbations together with the matter content perturbations, between the inflationary primordial phase of the universe and the observations performed today. We first consider the fluid approximation in order to extract the general leading behaviours. We then turn to the kinetic theory at second order, which is necessary in order to obtain the non-linear transfer function for radiation, in order to determine the non-Gaussianity in the cosmic microwave background.
We also study the linear perturbation theory around anisotropic universes. We set up the gauge invariant perturbation theory around a Bianchi I space-time, and we study the observational signatures of a model of inflation having this symmetry.