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Axion Mass Prediction from Adaptive Mesh Refinement Cosmological Lattice Simulations

Joshua N. Benabou1,2, Malte Buschmann3, Joshua W. Foster4,5, and Benjamin R. Safdi1,2

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Phys. Rev. Lett. 134, 241003 – Published 20 June, 2025

DOI: https://doi.org/10.1103/6v21-d6sj

Abstract

The quantum chromodynamics (QCD) axion arises as the pseudo-Goldstone mode of a spontaneously broken Abelian Peccei-Quinn (PQ) symmetry. If the scale of PQ symmetry breaking occurs below the inflationary reheat temperature and the domain wall number is unity, then there is a unique axion mass that gives the observed dark matter (DM) abundance. Computing this mass has been the subject of intensive numerical simulations for decades since the mass prediction informs laboratory experiments. Axion strings develop below the PQ symmetry-breaking temperature, and as the string network evolves, it emits axions that go on to become the DM. A key ingredient in the axion mass prediction is the spectral index of axion radiation emitted by the axion strings. We compute this index in this Letter using the most precise and accurate large-scale simulations to date of the axion-string network leveraging adaptive mesh refinement to achieve the precision that would, otherwise, require a static lattice with 262,1443 lattice sites. We find a scale-invariant axion radiation spectrum to within 1% precision and find no evidence that the spectral index of radiation evolves with time. Accounting for axion production from strings prior to the QCD phase transition leads us to predict that the axion mass should be approximately ma∈(45,65)  μeV. However, we provide preliminary evidence that axions are produced in greater quantities from the string-domain-wall network collapse during the QCD phase transition, potentially increasing the mass prediction to as much as 300  μeV.

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Phys. Rev. Lett. 134, 241003– Published 20 June, 2025
  • Received 13 January 2025
  • Revised 3 April 2025
  • Accepted 29 May 2025
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