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  • Open Access

Fast and accurate implementation of the effective fluid approximation for ultralight axions

Adam Moss*, Lauren Gaughan†, and Anne M. Green‡

  • *Contact author: adam.moss@nottingham.ac.uk
  • †Contact author: lauren.gaughan@nottingham.ac.uk
  • ‡Contact author: anne.green@nottingham.ac.uk
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Phys. Rev. D 111, 123530 – Published 17 June, 2025

DOI: https://doi.org/10.1103/fy1y-rjst

Abstract

We present a numerically efficient and accurate implementation of the Passaglia-Hu effective fluid approximation for ultralight axions within the Boltzmann code camb. This method is specifically designed to evolve the axion field accurately across cosmological timescales, mitigating the challenges associated with its rapid oscillations. Our implementation is based on the latest version of camb, ensuring compatibility with other cosmological codes., e.g., for calculating cosmological parameter constraints. Compared to exact solutions of the Klein-Gordon equation, our method achieves subpercent accuracy in the cosmic microwave background power spectrum across a broad range of axion masses, from 10−28  eV to 10−24  eV. We perform Markov chain Monte Carlo analyses incorporating our implementation, and find improved constraints on the axion mass and abundance compared to previous, simpler fluid-based approximations. For example, using Planck Public Release 4 and Dark Energy Spectroscopic Instrument baryon acoustic oscillation data, we find 2σ upper limits on the axion fraction fax<0.0082 and physical density Ωaxh2<0.0010 for m=10−28  eV.

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Information

Phys. Rev. D 111, 123530– Published 17 June, 2025
  • Received 29 January 2025
  • Accepted 2 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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