I briefly review some kind of imprints that a primordial magnetic
field can leave on the CMB and I show that these can be observed only
if their amplitude is greater than 10^-9 Gauss on the Mpc scale.
Then, I explain how they can be strongly constrained by a stochastic
background of gravity waves, going into the details of the so-called
gravito-magnetic interaction: the energy momentum tensor of a magnetic
field always contains a spin-2 component in its anisotropic stress and
therefore generates gravitational waves. This gravitional wave
production can be very strong and back-reaction cannot be neglected.
Moreover, given a gravitational wave background which affects the
evolution of magnetic fields, it has been argued in the literature
that this can lead to a very strong amplification of a primordial
magnetic field. I will finally revisit these claims and study
back-reaction to second order.
Reference:
C. Caprini and R. Durrer, Phys. Rev. D 65, 023517 (2001)
C.G.Tsagas, P.K.S.Dunsby and M.Marklund, "Gravitational wave
amplification of seed magnetic fields", Phys. Lett. B 561, 17 (2003)
[arXiv:astro-ph/0112560]
C. Tsagas, "Resonant amplification of magnetic seed fields by
gravitational waves in the early universe", Phys. Rev. D 72, 123509
(2005) [arXiv:astro-ph/0508556]
E.Fenu and R.Durrer, "Interactions of cosmological gravity waves and
magnetic fields", arXiv:0809.1383 [astro-ph]