Cosmological Aspects of the Clockwork Axion

The clockwork axion refers to a family of aligned multi-axion models that lead to an exponential hierarchy between the scale of Peccei-Quinn symmetry breaking and the scale of the axion decay constant. The clockworking can bring the Peccei-Quinn-scale particles to within reach of collider experiments.In this work we are interested in whether cosmological observations impose any new constraints on the clockwork axion. If the universe reheats above the scale of Peccei-Quinn breaking, then the ensuing cosmological phase transition produces a network of topological defects, which have a qualitatively different behavior from the string-wall network in the usual axion models. We estimate the relic abundances of axion dark matter and dark radiation that arise from the emission of axions by the defect network, and we infer a constraint on the scale of Peccei-Quinn breaking and the mass spectrum. We find that the defect contribution to the axion dark matter relic abundance is generally negligible. However, the defect production of relativistic axion dark radiation becomes significant if the scale of Peccei-Quinn symmetry breaking is larger than $100 \, {\rm TeV}$, and measurements of $\Delta N_{\rm eff}$ provide a new probe of this class of models.