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 [Formula: see text]. 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 accordance with the PLANCK and WMAP data.

中文翻译：

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非线性电动力学的宇宙膨胀

研究了具有二维参数的非线性电动力学。当因果性、单一性和经典稳定性原则成立时，电磁场的范围就得到了。我们的模型中不存在电荷中心的电场奇点，并且对库仑定律进行了修正[公式：见正文]。宇宙膨胀发生在随机磁场的背景下。宇宙演化的第二阶段是辐射时代，优雅的出口存在。我们根据 PLANCK 和 WMAP 数据估计了大致符合 PLANCK 和 WMAP 数据的光谱指数、张量与标量比以及光谱指数的运行。