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/ρ, remains close to 1/3 throughout the evolution of the universe if E²=B² in the late universe to a high degree of accuracy. Theories with electromagnetic Lagrangians of the form L=-1/4F²+αF⁴ have recently been studied in magnetic universes, where the electric field vanishes. It was shown that the F⁴ term can produce a bounce in the early universe, avoiding an initial singularity. Here I show that the inclusion of an electric field, with E²≃B² 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=-1/4F²-μ⁸/F², 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 E²<3B².