Homogeneous and isotropic cosmologies with nonlinear electromagnetic radiation

In this paper I examine cosmological models that contain a stochastic background of nonlinear electromagnetic radiation. I show that for Born-Infeld electrodynamics the equation of state parameter, w=P/, remains close to 1/3 throughout the evolution of the universe if E^2=B^2 in the late universe to a high degree of accuracy. Theories with electromagnetic Lagrangians of the form L=-14F^2+F^4 have recently been studied in magnetic universes, where the electric field vanishes. It was shown that the F^4 term can produce a bounce in the early universe, avoiding an initial singularity. Here I show that the inclusion of an electric field, with E^2B^2 in the late universe, eliminates the bounce and the universe begins with an initial singularity. I also examine theories with Lagrangians of the form L=-14F^2-^8/F^2, which have been shown to produce a period of late time accelerated expansion in magnetic universes. I show that, if an electric field is introduced, the accelerated phase will only occur if E^2<3B^2.