Maxwell-Kosteleck\'y Electromagnetism and Cosmic Magnetization
  The Lorentz violating term in the photon sector of Standard Model Extension, $\mathcal{L}_K = -{$\frac14$} (k_F)_{\alpha \beta \mu \nu} F^{\alpha \beta} F^{\mu \nu}$ (here referred to as the Kosteleck\'{y} term), breaks conformal invariance of electromagnetism and enables a superadiabatic amplification of magnetic vacuum fluctuations during inflation. For a wide range of values of parameters defining Lorentz symmetry violation and inflation, the present-day magnetic field can have an intensity of order of nanogauss on megaparsec scales and then could explain the large-scale magnetization of the universe. 
L. Campanelli and P. Cea