Universe inflation and nonlinear electrodynamics

Abstract

We analyse the inflation of the universe 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, and the condition for universe inflation is obtained. It is demonstrated that singularities of energy density and pressure are absent as the scale factor approaches zero. When the scale factor goes to infinity, we have the equation of state for the ultra-relativistic case. The curvature invariants do not possess singularities. The evolution of the universe shows that at large time scales, the scale factor corresponds to the radiation era. The duration of universe inflation is also analysed. We study the classical stability and causality by computing the speed of sound. Cosmological parameters including the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r, and the running of the spectral index αs\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _s$$\\end{document} are evaluated.