Luminosity distance for Born-Infeld electromagnetic waves propagating in   a cosmological magnetic background
  Born-Infeld electromagnetic waves interacting with a static magnetic background are studied in an expanding universe. The non-linear character of Born-Infeld electrodynamics modifies the relation between the energy flux and the distance to the source, which gains a new dependence on the redshift that is governed by the background field. We compute the luminosity distance as a function of the redshift and compare with Maxwellian curves for supernovae type Ia. 
Matias Aiello, Gabriel Bengochea, Rafael Ferraro