Abstract
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 TeV, and measurements of ΔNeff provide a new probe of this class of models.
Highlights
Previous studies of these defect networks have usually assumed fpq ∼ fg, but this relation is badly broken for the clockwork axion, and the presence of N + 1 complex scalar fields participating in the phase transition gives the defect network a much richer structure [20] than what is found in the usual QCD axion cosmology
The result is a suppression of the axion dark matter relic abundance arising from the defect network. (The relic abundance from the misalignment mechanism depends on the axion decay constant fg directly, and it is unaffected by the clockworking.) On the other hand, we find that axion emission from small-scale structure on the domain walls is still efficient, and this can give rise to a population of relativistic axions that contribute to the dark radiation
In this work we have explored some of the cosmological implications of the clockwork axion with a focus on the network of topological defects and their contribution to the axion relic abundance. (Other cosmological aspects of the clockwork axion are discussed in refs. [19,20,21].) The primary cosmological consequence of clockworking, which lowers fpq compared to fa, is to make it easier for the PQ symmetry to be restored when the universe reheats after inflation
Summary
The clockwork axion is a class of multi-axion models [12] with an exponentially large hierarchy between the PQ-breaking scale, fpq, and the axion decay constant, fa. Since we must allow πn(x) ∈ [0, 2πfpq) in order to span the full configuration space, the property On0 1 for n = N 1 requires the axion field range be exponentially large. A reasonable choice is to consider ψr in the same representation as the uR or dR quarks, which gives NDW = 1 and avoids color stable relics with mass mψ = yfpq, which are a potential disaster if PQ breaks after inflation. With this setup we can compute the axion mass; it is given by eq (1.1) where fg = fa
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