Large-scale magnetic fields from inflation due to a $CPT$-even   Chern-Simons-like term with Kalb-Ramond and scalar fields
  We investigate the generation of large-scale magnetic fields due to the breaking of the conformal invariance in the electromagnetic field through the $CPT$-even dimension-six Chern-Simons-like effective interaction with a fermion current by taking account of the dynamical Kalb-Ramond and scalar fields in inflationary cosmology. It is explicitly demonstrated that the magnetic fields on 1Mpc scale with the field strength of $\sim 10^{-9}$G at the present time can be induced. 
Kazuharu Bamba, C. Q. Geng, S. H. Ho and W. F. Kao
astro-ph.CO gr-qc hep-ph hep-th