Superconducting Cosmc Strings and Primordial Magnetic Fields

We consider grand unified theories with superconducting cosmic strings and which admit the mechanism for generating primordial magnetic fields recently discussed by Vachaspati. We show that these models are severely constrained by cosmological arguments. Quite generically, either stable springs or vortons will form. Provided the mass per unit length of the strings is sufficiently large, these stable configurations will overclose the Universe.