On the inflationary origin of primordial magnetic fields

Contrary to the conventional wisdom, we find that it is possible to generate coherent magnetic seed fields over a scale of 10 Mpc effciently via the spinodal instability during primordial inflation, provided that a fast-roll stage is involved before the inflaton enters into the slow-roll phase. However, the primordial magnetic field produced in such a mechanism is far too powerful to consistently fit into the energy constraint required by the scalar field driving the cosmic inflation.