In the simplest picture, the masses of string axions populating the axiverse depend on two parameters: the supersymmetry-breaking scale M susy and the action S of the string instantons responsible for breaking the axion shift symmetry. In this work, we explore whether cosmological data can be used to probe these two parameters. Adopting string-inspired flat priors on log 10 M susy and S and imposing that M susy be sub-Planckian, we find S = 198 ± 28 . These bounds suggest that cosmological data complemented with string-inspired priors select a quite narrow axion mass range within the axiverse, log 10 ( m a / eV ) = ? 21. 5 ? 2.3 + 1.3 . We find that M susy remains unconstrained due to a fundamental parameter degeneracy with S . We explore the significant impact of other choices of priors on the results, and we comment on similar findings in recent previous literature.
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