Resonant amplification of magnetic seed fields by gravitational waves in the early universe

Inflation is known to produce both gravitational waves and seed magnetic fields on scales well beyond the size of the horizon. The general relativistic study of the interaction between these two sources after the end of inflation, showed a significant amplification of the initial magnetic seed which brought the latter within the currently accepted dynamo limits. In the present article we revisit this gravitomagnetic interaction and argue that the observed strong growth of the field is the result of resonance. More specifically, we show that the maximum magnetic boost always occurs when the wavelength of the inducing gravitational radiation and the scale of the original seed field coincide. We also look closer at the physics of the proposed Maxwell-Weyl coupling, consider the implications of finite electrical conductivity for the efficiency of the amplification mechanism and clarify further the mathematics of the analysis.