Étude de quelques modèles cosmologiques dans le cadre de la théorie Einstein-Cartan.

Abstract

In this thesis, we have studied a few cosmological models in the framework of the Einstein-Cartan theory, that is to say, by including another geometric properties of space-time which is the torsion . We first treated the Kottler spherical symmetric static model in the case of a ompletely antisymmetric Cartan tensor. In addition to being the only case with physical significance, it allows autoparalleles to coincide with geodesics. Using the covariant non-conservation equation, a feature that differentiates the Einstein-Cartan theory from general relativity, it has been shown that the weak Gauss law is no longer true. This mechanism allowed us to hypothesize that torsion could be an alterative to dark matter. It was then shown that the effect of this torsion could dominate that of the cosmological constant in the phenomenon of the deflection of light by a gravitational lens. Another model of interest in this thesis is that of Einstein-Strauss, which connects Kottler’s metric inside the Schücking sphere to the Robertson-Walker metric outside the Schücking sphere. this. Taking into account the spacetime twist generated by the material distribution, we have encountered a mass problem which proves to be variable in this case, which represents a violation of the principle of mass conservation.