Gauge invariant nonlinear electrodynamics motivated by a spontaneous breaking of the Lorentz symmetry

We introduce a new version of nonlinear electrodynamics which is produced by a spontaneous symmetry breaking of Lorentz invariance induced by the nonzero vacuum expectation value of the gauge invariant electromagnetic field strength. The symmetry breaking potential is argued to effectively arise from the integration of massive gauge bosons and fermions in an underlying fundamental theory. All possible choices of the vacuum lead only to the remaining invariant subgroups T(2) and HOM(2). We explore in detail the plane wave solutions of the linearized sector of the model for an arbitrary vacuum. They present two types of dispersion relations. One corresponds to the case of the usual Maxwell electrodynamics with the standard polarization properties of the fields. The other dispersion relation involves anisotropies determined by the structure of the vacuum. The corresponding fields reflect these anisotropies. The model is stable in the small Lorentz invariance violation (LIV) approximation. We have also embedded our model in the photon sector of the standard model extension, in order to translate the many bounds obtained in the latter into corresponding limits for our parameters. The one-way anisotropic speed of light is calculated for a general vacuum, and its isotropic component is strongly bounded by δ-tildec/c<2x10-32. The anisotropic violation contribution is estimated by introducing an alternative definition for the difference of the two-way speed of light in perpendicular directions, Δc, that is relevant to Michelson-Morley type of experiments and which turns out to be also strongly bounded by Δc/c<10-32. Finally, we speculate on the relation of the vacuum energy of the model with the cosmological constant and propose a connection between the vacuum fields and the intergalactic magnetic fields.