Universe inflation and nonlinear electrodynamics

WE analyse the universe inflation when the source of gravity is electromagnetic fields obeying nonlinear electrodynamics with two parameters and without singularities. The cosmology of the universe with stochastic magnetic fields is considered. The condition for the universe inflation is obtained. It is demonstrated that singularities of the energy density and pressure are absent as the scale factor approaches to zero. When the scale factor goes to infinity one has equation of state for ultra-relativistic case. The curvature invariants do not possess singularities. The evolution of universe is described showing that at large time the scale factor corresponds to the radiation era. The duration of universe inflation is analysed. We study the classical stability and causality by computing the speed of the sound. Cosmological parameters such as the spectral index $n_s$, the tensor-to-scalar ratio $r$ and the running of the spectral index $\alpha_s$ are evaluated.