Global dynamics for a charged and colliding plasma in presence of a massive scalar field on the Robertson–Walker spacetime

Abstract

We consider the coupled Einstein–Maxwell–Boltzmann system with cosmological constant in presence of a massive scalar field. The background metric is that of Friedman–Lemaitre–Robertson–Walker space time in the spatially homogeneous case where the unknown functions only depend on time and not on the space variables $$(x^i)$$ , $$i=1,2,3$$ . By combining the energy estimates method with that of characteristics we derive under suitable conditions on the collision kernel [see (2.20)], a local (in time) solution of the coupled system. Further, under the hypotheses that the data are small in some appropriate norms and that the cosmological constant satisfies $$\Lambda > -4\pi m^2\Phi _0^2$$ , we derive a unique global (in time) solution (Theorem 6.1).