Primordial Magnetic Fields via Spontaneous Breaking of Lorentz Invariance

Spontaneous breaking of Lorentz invariance compatible with observational limits may realistically take place in the context of string theories, possibly endowing the photon with a mass. In this process the conformal symmetry of the electromagnetic action is broken allowing for the possibility of generating large scale ($\sim Mpc$) magnetic fields within inflationary scenarios. We show that for reheating temperatures safe from the point of view of the gravitino and moduli problem, $T_{RH} \laq 10^{9} GeV$ for $m_{3/2} \approx 1 TeV$, the strength of the generated seed fields is, in our mechanism, consistent with amplification by the galactic dynamo processes and can be even as large as to explain the observed galactic magnetic fields through the collapse of protogalactic clouds.