Axion string cosmology and its controversies

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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 $\ma\sim 100μ{\rm eV}$ with large specified uncertainties. We discuss critically the various suggestions in the literature that the axion mass migh be lighter.
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