Small explicit Peccei-Quinn breaking introduces a mass scale μ that can dominate early axion dynamics, causing the string-wall network to annihilate earlier and making relic abundance depend on both μ and f_a rather than f_a alone.
Stud- ies of the motion and decay of axion walls bounded by strings,
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On the predictivity of axion dark matter in the presence of Peccei-Quinn breaking
Small explicit Peccei-Quinn breaking introduces a mass scale μ that can dominate early axion dynamics, causing the string-wall network to annihilate earlier and making relic abundance depend on both μ and f_a rather than f_a alone.