How to obtain slow roll inflation driven by non-linear electrodynamics

We establish for the first time the conditions that must be imposed on the action for a magnetic universe in a theory of non-linear electrodynamics in order to have an asymptotically de Sitter initial state followed by a slow roll inflationary phase. We show that models so far proposed in the literature do not allow for a prolonged inflationary phase consistent with observations. We construct a Lagrangian that reduces to the Maxwell one in weak field; this is the only class of models that satisfies the required conditions for slow roll in the early Universe.