Bosonic superconducting cosmic strings. Pt. 1

This paper explores a four-dimensional field theory in which superconducting bosonic cosmic strings can form. We solve the field equations and explore the parameter space within thich the strings are superconducting. We find that the maximum allowed current is often much less than suggested by dimensional analysis. In most of the parameter space, even the maximum current in the strings is not sufficient for many of their proposed astrophysical uses and especially, the current is rarely sufficient to form 'frozen' string loops. (orig.)