Axion String Constraints

We study the production of cosmological axions in the standard scenario in which a global string network forms at the Peccei-Quinn phase transition. We make detailed calculations of the axions produced by string loops, comparing these with estimates of other contributions from long strings and domain walls. We delineate key uncertainties in string network evolution, the chief of which is the magnitude of radiative backreaction. We conclude that axions produced by these topological contributions provide the significant cosmological constraint on the symmetry breaking scale $f_a$ and the axion mass $m_a$.