Generation of scale invariant magnetic fields in bouncing universes

Understand

We consider the generation of primordial magnetic fields in a class of bouncing models when the electromagnetic action is coupled non-minimally to a scalar field that, say, drives the background evolution.

• For scale factors that have the power law form at very early times and non-minimal couplings which are simple powers of the scale factor, one can easily show that scale invariant spectra for the magnetic field can arise before the bounce for certain values of the indices involved.
• It will be interesting to examine if these power spectra retain their shape after the bounce.
• However, analytical solutions for the Fourier modes of the electromagnetic vector potential across the bounce are difficult to obtain.