The study used the updated Pantheon+ dataset, comprising 1,550 unique Type Ia supernovae from 20 surveys across redshifts 0.001 < z < 2.27. The authors divided the data into six subsamples—Low-z, PS1, SDSS, SNLS, DES and High-z—and repeatedly removed each one to assess its influence. Although the expanded Low-z group has a nearly uniform sky distribution, several other groups are strongly localized: SDSS occupies a narrow stripe, SNLS is concentrated in approximately four directions, DES lies within four fields, PS1 spans about ten regions, and High-z is scattered across nine directions.

For the dipole-fitting analysis, the researchers modified the theoretical distance modulus with a directional term and fitted the dipole amplitude and Galactic coordinates alongside the matter density, Hubble constant and absolute magnitude. Markov Chain Monte Carlo sampling using the emcee package explored the parameter space. For the complete Pantheon+ sample, the dipole amplitude was constrained only by a 95% confidence upper limit of A_D < 0.764 × 10⁻³. The associated direction was (l, b) = (138.39°, 8.53°), consistent with a statistically weak anisotropy signal.

The low-redshift subsample produced a more distinct result. Its dipole amplitude was A_D = 0.952 with uncertainties of +0.454 and −0.403, all in units of 10⁻³, and pointed toward (l, b) = (149.77°, −12.20°). The signal was concentrated mainly in a combined subset of surveys 5, 56, 63 and 150, for which the amplitude was A_D = 1.730 with uncertainties of +0.554 and −0.715, also in units of 10⁻³. That direction, (153.05°, −1.25°), was separated from the low-redshift direction by 11.42 degrees and from the full-sample direction by 15.45 degrees. Removing the Low-z group from the full compilation shifted the fitted dipole direction by 138.07 degrees, whereas removing PS1, SDSS, SNLS, DES or High-z individually left the result broadly consistent with the full-sample analysis.

The researchers evaluated the low-redshift dipole results with 5,000 isotropic mock samples generated under a flat Lambda-CDM model with the dipole amplitude fixed at zero. Mock samples retained the observed redshifts, sky positions, calibrator flags and covariance matrix, with Gaussian fluctuations added to the isotropic predictions. The empirical Delta chi-squared test yielded a p-value of 0.0116 for the full Low-z group, corresponding to a Gaussian-equivalent one-sided significance of 2.27 sigma. The four-survey subset produced a p-value of 0.0026, or 2.79 sigma. Both datasets covered the redshift interval 0.001 < z < 0.093, so these estimates characterize a nearby, subset-dependent signal rather than a uniform feature across the compilation.

The second method divided the sky into opposing hemispheres, fitted the matter density separately in each and defined the anisotropy level from the fractional difference between the two best-fit values. The search used 196,608 random orientations. For the full sample, the maximum anisotropy level was AL_max = 0.289 ± 0.052, directed toward (l, b) = (127.97°, 17.90°). A separate mock analysis generated 500 realizations by randomizing only the supernova sky positions while retaining other data properties. The resulting p-value of 0.060 corresponded to a one-sided 1.56-sigma significance, providing weak evidence for anisotropy in the complete sample.

Subsample exclusions showed that the hemisphere result was also sensitive to the uneven distribution of observations. Removing Low-z increased AL_max to 0.426 ± 0.068, while removing PS1, SDSS, SNLS, DES or High-z individually produced maximum levels consistent with the full value within one standard deviation. Removing Low-z, SNLS or High-z changed the preferred direction by 72.82, 38.97 and 51.96 degrees, respectively, whereas exclusions of PS1, SDSS and DES shifted it by only 0.67, 0.45 and zero degrees. Along the full-sample axis, Low-z and High-z contributed negative anisotropy levels of −1.385 and −0.737, while SNLS contributed a positive value of 0.376.

Analyses of individual and combined groups reinforced the link between the preferred direction and the SNLS subsample. SNLS alone yielded AL_max = 0.813 ± 0.216 toward (132.19°, 16.02°), only 4.45 degrees from the full-sample direction. The combined Low-z and High-z group favored a direction 90.22 degrees away from the full-sample result, but adding SNLS changed the separation to 1.48 degrees. The authors therefore associate the full-sample hemisphere direction primarily with SNLS, while the Low-z and High-z groups contribute in the opposing direction along that axis.

Taken together, the two analyses did not provide robust evidence for an intrinsic cosmic anisotropy in the full Pantheon+ sample. The dipole signal was concentrated in low-redshift data from a small combination of surveys, whereas the hemisphere-comparison direction was mainly associated with the inhomogeneously distributed SNLS data. Because both findings varied substantially with subsample selection, the study favors an explanation involving local structures or the distribution of observations over an intrinsic preferred direction in cosmic expansion. The analysis used existing public data and did not generate new observations, so its conclusions are bounded by the compilation’s spatial coverage and the sensitivity of the two methods to its survey composition.

Subject of Research: Cosmic anisotropy in the Pantheon+ Type Ia supernova compilation

Article Title: Revisiting cosmic anisotropy with the Pantheon+ compilation

Article References: Zhou, Y., & Zhao, D. (2026). Revisiting cosmic anisotropy with the Pantheon+ compilation. The European Physical Journal C, 86(10), Article 1181. https://doi.org/10.1140/epjc/s10052-026-16465-7

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16465-7

Keywords: Pantheon+, Type Ia supernovae, cosmic anisotropy, dipole fitting, hemisphere comparison, supernova surveys, SNLS, low-redshift cosmology, isotropic simulations, Revisiting, cosmic, anisotropy