Gauge invariant wave equations in curved space-times and primordial magnetic fields

Abstract

The inflationary production of magnetic field seeds for galaxies is discussed. The analysis is carried out by writing the wave equation of the electromagnetic field in curved space-times. The conformal invariance is broken by taking into account the interaction of the electromagnetic field with the curvature tensor of the form $\ensuremath{\lambda}{R}_{\ensuremath{\alpha}\ensuremath{\beta}\ensuremath{\gamma}\ensuremath{\delta}}{F}^{\ensuremath{\alpha}\ensuremath{\beta}}{F}^{\ensuremath{\gamma}\ensuremath{\delta}}$. Such a term induces an amplification of the magnetic field during the reheating phase of the universe, but no growth of the magnetic field occurs in the de Sitter epoch. The resulting primordial magnetic field turns out to have strengths of astrophysical interest.