Equations d’einstein-vlasov en symetrie t² avec champ scalaire non lineaires

Abstract

We study in this work, the local and uniqueness of solutions of the non-linear Einstein-Vlasov scalar field system with T2 symmetry, in contracting direction and the expanding direction. We use the conformal coordinates and areal coordinates respectively in contracting and expanding direction. So, we prove in the case of cosmological models for the Einstein-Vlasov-scalar field system with T2 symmetry, that the solutions exist globally in the past and the future. The sources of the equations are generated by a distribution function and a scalar field, subject to the Vlasov and the wave equations respectively. Starting from the fact that some matter are not taken into account, in the expanding of Universe. We add dark and dark energy, which represents more than two thirds of the total available matter of the Universe.That we model we non linear scalar Field and potential.