Interactions of cosmological gravitational waves and magnetic fields

The energy momentum tensor of a magnetic field always contains a spin-2 component in its anisotropic stress and therefore generates gravitational waves. It has been argued in the literature (Caprini and Durrer [C. Caprini and R. Durrer, Phys. Rev. D 65, 023517 (2001)]) that this gravitational wave production can be very strong and that backreaction cannot be neglected. On the other hand, a gravitational wave background does affect the evolution of magnetic fields. It has also been argued (Tsagas et al. [C. G. Tsagas, P. K. S. Dunsby, and M. Marklund, Phys. Lett. B 561, 17 (2003)] [C. Tsagas, Phys. Rev. D 72, 123509 (2005)]) that this can lead to a very strong amplification of a primordial magnetic field. In this paper we revisit these claims and study backreaction to second order.