Duality and scale invariant magnetic fields from bouncing universes

TL;DR

This paper analytically investigates the generation of scale-invariant magnetic fields in bouncing universes with non-minimal coupling, revealing spectrum preservation across the bounce and invariance under certain transformations, but also highlighting backreaction issues.

Contribution

It provides an analytical evaluation of magnetic and electric field spectra in bouncing cosmologies with non-minimal coupling, extending previous numerical results and exploring invariance properties.

Findings

Spectrum shape is preserved across the bounce for small wavenumbers.

Backreaction becomes severe at the bounce.

Magnetic field power spectrum is invariant under specific coupling transformations.

Abstract

Recently, we had numerically shown that, for a non-minimal coupling that is a simple power of the scale factor, scale invariant magnetic fields arise in a class of bouncing universes. In this work, we {\it analytically} evaluate the spectrum of magnetic and electric fields generated in a sub-class of such models. We illustrate that, for cosmological scales which have wavenumbers much smaller than the wavenumber associated with the bounce, the shape of the spectrum is preserved across the bounce. Using the analytic solutions obtained, we also illustrate that the problem of backreaction is severe at the bounce. Finally, we show that the power spectrum of the magnetic field remains invariant under a two parameter family of transformations of the non-minimal coupling function.