Cosmological evolution for magnetic universe based in a simple nonlinear electrodynamics

We investigate the cosmic dynamics of Friedmann-Robertson-Walker universes - flat spatial sections - which are driven by nonlinear electrodynamics (NLED) Lagrangian. We pay special attention to the check of the sign of the square sound speed since, whenever the latter quantity is negative, the corresponding cosmological model is classically unstable against small perturbations of the background energy density. Besides, based on causality arguments, one has to require that the mentioned small perturbations of the background should propagate at most at the local speed of light. We also look for the dynamics by mean of dynamical system tools. Our results indicate that in the case of the power law NLED Lagrangian, it is not possible to explain the current accelerated expansion stage of the universe because the model is not stable for the possible values of the free parameter that allows such expansion. Finally, in the second case, whose Lagrangian has a power law NLED term plus a Maxwell term, the model is stable and causal for a certain range of values of the free parameter.