Primordial magnetic fields from gravitationally coupled electrodynamics in nonsingular bounce cosmology

Abstract

We in this paper study a class of mechanism of the production of the primordial magnetic field (PMF) in the non-singular bouncing cosmology, through the coupling of the electromagnetic field to gravity. We adopt an electrodynamic model with a coupling coefficient as a function of the scale factor $a$, i.e., $f=1+(a/a_\star)^{-n}$, with $a_\star$ and $n>0$ being constants.With analytical calculations, we find that this model can yield a blue tilted power spectrum of PMF on large scales from 1 Mpc to the Hubble length if the bounce scenario has experienced a contracting phase with an equation-of-state parameter larger than $-1/3$. Furthermore, in order to satisfy the constraints of observational data, the present mechanism favors the so-called ekpyrotic-bounce paradigm.The back-reaction of the energy density of PMF at the bouncing point can lead to additional theoretical constraints on the underlying bouncing paradigm.