Non-uniform Acceleration: Does the Universe's Expansion Depend on Direction? ✦
A hemispherical analysis of the deceleration parameter q₀ was performed using the Pantheon+ supernova sample to test the isotropy of cosmic acceleration and the reliability of redshift corrections. Directional variations in q₀ were found: even in the z_HD frame, where the CMB dipole and peculiar velocities are accounted for, a dipole anisotropy persists with Δq₀ = 0.112 and S/N = 2.155, aligned with the CMB dipole direction and weakening as the minimum redshift increases. From the supernova data, the local motion velocity was determined as v⊙ = 307.26^{+32.00}_{-22.28} km/s in the direction (RA, DEC) = (156.40, -3.38)°, deviating from the Planck CMB dipole by ~1.9σ. When this dipole is included in the redshift correction procedure, the anisotropy is suppressed: the dipole vanishes, the maximum S/N drops to ≲1.75, and fluctuations become statistically insignificant. This points to a residual large-scale flow unaccounted for in velocity field models, and a systematic uncertainty in supernova cosmology at low z.
Context
The cosmological principle—the cornerstone of modern cosmology—states that the Universe is homogeneous and isotropic on large scales. In the standard model ΛCDM, the accelerated expansion discovered through type Ia supernovae in 1998 by Saul Perlmutter, Brian Schmidt, and Adam Riess is described by dark energy. The deceleration parameter q0 (which indicates whether expansion is slowing down or speeding up) should be a single number for the whole sky. Any statistically significant variation of q0 with direction would be a red flag. And such flags have been raised: earlier hints of a dipole anisotropy—a preferred axis roughly aligned with the Solar System's motion relative to the cosmic background—were found in redshift data of supernovae and the cosmic microwave background. This could point either to a 'tilted' cosmology, where we are not at rest with respect to the mean flow, or to systematics in data processing.
Methods
The authors used the latest Pantheon+ compilation—1701 type Ia supernovae with precisely measured redshifts and light curves from photometry and spectroscopy. For each of 450 directions on the sky, they split the sample into two hemispheres and independently determined q0 in each, using a cosmographic expansion of the apparent magnitude (without assuming a specific cosmological model). Then they computed the difference Δq0 between opposite hemispheres and its statistical significance (signal-to-noise). The analysis was performed for three redshift frames: heliocentric (z_hel), in the rest frame of the cosmic microwave background (z_CMB), and with additional correction for galaxy peculiar velocities (z_HD) according to the velocity field reconstruction from the 2M++ survey. To check sensitivity, the authors also derived an effective motion dipole directly from the supernova data by minimizing the anisotropy, and recomputed z_HD with this dipole.
Results
In the z_HD frame, which is considered the cleanest of kinematic effects, a dipole anisotropy in q0 still appeared: the maximum difference Δq0 = 0.112 (with a signal-to-noise of 2.155) in a direction close to the CMB dipole. This means q0 is more negative (acceleration is stronger) in the same direction we are moving. When progressively removing more distant supernovae (raising the minimum redshift to 0.07), the signal weakened and became indistinguishable from noise. In the heliocentric and z_CMB frames, the anisotropy was much more pronounced—corrections for the Sun's motion and peculiar velocities do smooth the picture, but not completely. When the authors let the data themselves choose the optimal motion dipole, they obtained a speed v = 307 (+32/-22) km/s in a direction shifted by about 1.9σ from the Planck dipole (369.82 ± 0.11 km/s). Using this 'supernova' dipole for redshift correction, the q0 anisotropy practically vanished: maximum signal-to-noise dropped to ≲1.75, and the residual map became patchy, without a preferred direction. This indicates that the original anisotropy was generated by residual systematics in the modeling of peculiar velocities, in particular an unaccounted coherent bulk flow of order 100 km/s.
Implications
The main takeaway: the statistically significant anisotropy of the acceleration parameter is most likely not evidence for a violation of the cosmological principle, but reflects our imperfect knowledge of the local velocity field. Even state-of-the-art reconstructions like those in Pantheon+ do not fully capture the collective motions of galaxies on scales of hundreds of millions of light-years. This underscores how carefully we must interpret searches for 'cosmic dipoles'—they can arise because we choose the wrong reference frame. For cosmology relying on supernovae as standard candles, this means an additional systematic uncertainty in determining dark energy parameters, including the Hubble constant, at the level of Δq0 ≈ 0.01–0.04 depending on the reference frame.
Future development
The next generation of surveys—such as the Vera Rubin Observatory (LSST) and the Nancy Grace Roman Space Telescope—will provide much denser and more uniform sky coverage with supernovae, enabling isotropy tests at far higher precision. In parallel, methods for reconstructing the velocity field from galaxy distribution data and machine learning will improve, helping to separate kinematic effects from genuine cosmological anisotropy. It is not impossible that a small residual signal does point to new physics—for instance, a 'dark flow' or anisotropic dark energy.
Impact
The results directly affect cosmology, especially the measurement of the Hubble constant and the equation of state of dark energy via supernovae. They are also important for interpreting other dipole anomalies observed in the cosmic microwave background, the distribution of quasars, and radio galaxies.
Next steps
It is necessary to revisit the systematics of peculiar velocity corrections at low redshifts, possibly including an additional bulk flow as a free parameter. It would also be desirable to repeat the analysis on independent supernova samples and using the full covariance matrix recalculated for a variable dipole.
Key open problems
This work touches on several open problems: the validity of the cosmological principle, the nature of dark energy (could it be anisotropic?), the origin of the 'cold spot' and other CMB anomalies, and the so-called 'dipole problem'—the discrepancy between the dipole measured from the CMB and that derived from the distribution of distant radio sources.
🎯 Did you know that our Solar System is zooming through the Universe at about 370 km/s relative to the cosmic microwave background? That's about 1.3 million km/h! This 'tailwind' is what causes most of the observed anisotropies in cosmological parameters if not carefully subtracted.
🎬 In Liu Cixin's sci-fi novel 'The Dark Forest,' the universe is far from homogeneous—it harbors 'dark' regions with unknown properties. Our work reminds us that in real space too, apparent anisotropy may be a clue to hidden patterns, even if we currently dismiss it as a measurement artifact.
Key numbers
- Δq0 максимум: 0.112
- Сигнал/шум максимум: 2.155
- Скорость диполя сверхновых: 307 км/с
- Остаточный объёмный поток: ~100 км/с
- Диполь реликтового излучения (Планк): 369.82 км/с