  Nonlinear electrodynamics with two dimensional parameters is studied. The
range of electromagnetic fields when principles of causality, unitarity and the
classical stability hold, are obtained. A singularity of the electric field at
the center of charges is absent within our model and there are corrections to
the Coulomb law as $r\rightarrow\infty$. The universe inflation takes place in
the background of stochastic magnetic fields. The second stage of the universe
evolution is the radiation era so that the graceful exit exists. We estimated
the spectral index, the tensor-to-scalar ratio, and the running of the spectral
index that are in a rough accord with the PLANCK and WMAP data.
