Primordial magnetic fields from gravitationally coupled electrodynamics in nonsingular bounce cosmology

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?)^(-n), with a? 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.