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Spectrum of axions in a scaling string network

José Correia1,2,*, Mark Hindmarsh2,3,†, Joanes Lizarraga4,5,‡, Asier Lopez-Eiguren4,5,§, Kari Rummukainen2,∥, and Jon Urrestilla4,5,¶

  • *Contact author: joserco@astro.uio.no
  • †Contact author: mark.hindmarsh@helsinki.fi
  • ‡Contact author: joanes.lizarraga@ehu.eus
  • §Contact author: asier.lopez@ehu.eus
  • ∥Contact author: kari.rummukainen@helsinki.fi
  • Contact author: jon.urrestilla@ehu.eus
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Phys. Rev. D 114, 063550 – Published 28 September, 2026

DOI: https://doi.org/10.1103/9m13-dqmv

Abstract

We report on measurements of axion spectra and their unequal time correlators in simulations on 12 2883 fixed grids, the largest such measurements to date. We use a novel combination of the fields that allow us to better distinguish the contributions from propagating axions from the contributions from strings, showing that previous measurements of the axion energy spectrum are approximately 30% derived from the string fields. We conclude that axion emission from a scaling string network is close to scale invariant (q≳1 in the standard parametrization), and that the energy spectrum of subhorizon modes behaves as paxln(kτ), where k is the comoving wave number, τ the conformal time, and pax≃10. The number density spectrum evolves towards a single curve for kτ≲102, with higher wave number deviations arising from initial conditions and resonant axion production at the string width scale. Our results are consistent with scaling framework, in which the total number density of axions produced from strings is nax=1.66(17)fa2H, where fa is the axion decay constant and H the Hubble rate. To interpret these results, we develop a simple analytic model based on an ensemble of string segments. The model reproduces the main features of the measured spectra and unequal-time correlators, and predicts q≤1, leaving q=1 as the only value consistent with theory and measurement. We report on axion production from the final collapse of the network in a future work.

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Phys. Rev. D 114, 063550– Published 28 September, 2026
  • Received 22 January 2026
  • Accepted 20 August 2026
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