We discuss the possible sources of dark matter axions in the early universe.
In the standard thermal scenario, an axion string network forms at the
Peccei-Quinn phase transition T\sim \fa and then radiatively decays into a
cosmological background of axions; to be the dark matter, these axions must
have a mass \ma \sim 100 \mu eV with specified large uncertainties. An
inflationary phase with a reheat temperature below the PQ-scale T_{reh} \lapp
\fa can also produce axion strings through quantum fluctuations, provided that
the Hubble parameter during inflation is large H_1 \gapp \fa; this case again
implies a dark matter axion mass \ma \sim 100 \mu eV. For a smaller Hubble
parameter during inflation H_1 \lapp \fa, `anthropic tuning' allows dark
matter axions to have any mass in a huge range below \ma\lapp 1 meV.Comment: to be published in the proceedings of the 5th IFT Workshop on Axion