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We review current cosmological constraints on the axion. We describe the basic mechanisms by which axions are created in the early universe, focussing on the standard thermal scenario where the dominant process is through axion radiation by a string network. A dark matter axion in this case would have a mass , with specified large uncertainties. This cosmological lower bound leaves a viable window for the axion below the astrophysical upper limit, . We also discuss alternative axion cosmologies which allow a much wider, but indefinite, mass range.

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