How isotropic is dark energy?

TL;DR

This paper investigates the isotropy of dark energy within anisotropic cosmological models, finding that certain anisotropic models can improve data fit but often violate CMB constraints, though constrained models can reconcile these issues.

Contribution

It introduces a parameterization of anisotropic stress in Bianchi I models that satisfies CMB quadrupole constraints while fitting late-time expansion data.

Findings

Anisotropic models can improve fit to SNe and BAO data.

Unconstrained anisotropic models violate CMB quadrupole bounds.

Constrained anisotropic models reconcile data fit with CMB constraints.

Abstract

Tensions in late-time expansion data have renewed interest in models beyond $\Lambda$CDM. We ask: \emph{how isotropic must dark energy be?} Working in Bianchi~I, we allow time-dependent anisotropic stress and introduce a parameterisation that enforces a vanishing line-of-sight integral of the shear, thereby satisfying the CMB ISW quadrupole bound by construction. Using Pantheon+SH0ES SNe together with DESI BAO distances, single-bin (constant) and five-bin anisotropic models improve the fit over $w$CDM by $\Delta(-2\ln L_{\rm iso})=14.8$ and $26.6$ respectively, but both violate the quadrupole constraint. In contrast, a five-bin constrained model achieves $\Delta(-2\ln L_{\rm iso})=15.4$ 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 $H_0$ value and DESI BAO distances.