Averaged properties of inhomogeneous models in relativistic cosmology
The standard cosmological model possesses some shortcomings for a relevent description of our universe and its constituents. First, it leaves in suspense the explanation of the origin of dark matter and dark energy. These components, introduced ad hoc in order to fit the observations, represent about 95% of the total energy. A second issue concerns the scale-independence of the model: whatever the scale of the considered system, it is expected identical dynamics and geometry. It is advisable to abandon the standard model and to focus on inhomogeneous cosmologies, and their average evolution. According to this formalism, inhomogeneities within a chosen scale globally impact on the dynamics of this latter through a so-called backreaction effect. This very rich approach also proposes an elegant explanation for the problem of the dark constituents: both stand for an effective manifestation of the inhomogeneities in the distributions of matter and geometry. This thesis focusses on the properties of averaged inhomogeneous models in general relativity. We first propose to describe the global behaviour of inhomogeneities according to a Chaplygin evolution, and according to a Ginzburg-Landau evolution. We also show the global gravitational instability of Friedmann-Lemaître-Robertson-Walker solutions. This class of solutions is already known to be locally gravitationaly unstable under the introduction of perturbations; here we show qualitatively that it does not furnish, in general, a good approximation as a physical background. We finally present a new relativistic perturbative scheme, in which scalar inhomogeneities evolve on a general background rather than on a pre-defined Friedmann-Lemaître-Robertson-Walker background. This new study extends the framework of application for inhomogeneous cosmologies, and may possibly explain the large-scale structure formation without the need for dark energy