Global Dynamics for a relativistic charged and colliding plasma in presence of a massive scalar field on the Robertson-Walker spacetime

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-Lema^itre-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 chock kernel (see Eq. 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 $\mathrm{\Lambda }>-4\pi m^2{\mathrm{\Phi }}_0^2$, we derive a unique global (in time) solution (Theorem 6.1).