On the self-consistence of electrodynamics in the early universe

The issue of a self-consistent solution of Maxwell-Einstein equations achieves a very simple form when all quantum effects are neglected but a weak vacuum polarization due to an external magnetic field is taken into account. From a semi-classical point of view this means to deal with an appropriate limit of the one-loop effective Lagrangian for electrodynamics. When the corresponding stress-energy tensor is considered as a source of the gravitational field a surprisingly bouncing behavior is obtained. The present toy model leads to important new features which should have taken place in the early universe.