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How isotropic is dark energy?

Richard A. Battye1,* and Adam Moss2,†

  • *Contact author: richard.battye@manchester.ac.uk
  • †Contact author: adam.moss@nottingham.ac.uk
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Phys. Rev. D 113, 123533 – Published 17 June, 2026

DOI: https://doi.org/10.1103/7195-wl39

Abstract

Tensions in late-time expansion data have renewed interest in models beyond ΛCDM. We ask: how isotropic must dark energy be? Working in Bianchi I, we allow time-dependent anisotropic stress and introduce a parametrization that enforces a vanishing line-of-sight integral of the shear, thereby satisfying the CMB integrated Sachs–Wolfe quadrupole bound by construction. Using Pantheon+SH0ES SNe together with Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation (BAO) distances, single-bin (constant) and five-bin anisotropic models improve the fit over wCDM by Δ(−2lnLiso)=14.8 and 26.6, respectively, but both violate the quadrupole constraint. In contrast, a five-bin constrained model achieves Δ(−2lnLiso)=15.4 while remaining compatible with the quadrupole limit. The fit improvement arises from two sources: capturing directional structure in the Pantheon+SNe data, and partially alleviating the tension between the SH0ES H0 value and DESI BAO distances.

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Phys. Rev. D 113, 123533– Published 17 June, 2026
  • Received 11 February 2026
  • Accepted 8 May 2026
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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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