Axion string cosmology and its controversies

Understanding axion cosmology has important experimental consequences since it constrains the range of allowed values for the axion mass. In the standard thermal scenario, which assumes Peccei-Quinn symmetry restoration after inflation, an axion string network forms at the phase transition $T\sim\fa$ and then radiatively decays into a cosmological background of axions. Under standard assumptions for the evolution of this string network and the radiation from it, axions must have a mass of $\ma\sim 100\mu{\rm eV}$ with large specified uncertainties. We discuss critically the various suggestions in the literature that the axion mass migh be lighter.