If Peccei-Quinn (PQ) symmetry is broken after inflation, the initial axion angle is a random variable on cosmological scales; based on this fact, estimates of the relic-axion mass density give too large a value if the axion mass is less than about ${10}^{\mathrm{-}6}$ eV. This bound can be evaded if the Universe underwent inflation after PQ symmetry breaking and if the observable Universe happens to be a region where the initial axion angle was atypically small, ${\mathrm{\theta }}_1$≲[${\mathit{m}}_{\mathit{a}}$/(${10}^{\mathrm{-}6}$ eV${]}^{0.59}$.] We show consideration of fluctuations induced during inflation severely constrains the latter alternative.

• Received 26 September 1990

DOI:https://doi.org/10.1103/PhysRevLett.66.5