We consider the possibility of generation of the primordial magnetic field on inflation and show that the effect of the back reaction of this field can be very important. Assuming that the back reaction does not spoil inflation we find a rather strong restriction on the amplitude of the primordial field which could be generated on inflation. Namely, this amplitude recalculated to the present epoch cannot exceed 10 −32 G in Mpc scales. This field seems to be too small to be amplified to the observable values by a possible dynamo mechanism.
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