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Study of Anisotropy in a Dark Energy Model with Latest Observations

This study extends the sign-switching dark energy model (ΛsCDM) to include anisotropic expansion, finding that while the anisotropy parameter is tightly constrained to be negligible, the framework effectively alleviates the Hubble tension to the 3.7σ level and is strongly favored over standard ΛCDM by recent cosmological observations.

Original authors: Manish Yadav, Archana Dixit, Pardeep Pardeep, Anirudh Pradhan, M. S. Barak

Published 2026-09-17

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CC BY 4.0

Original authors: Manish Yadav, Archana Dixit, Pardeep Pardeep, Anirudh Pradhan, M. S. Barak

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

For decades, the most successful story we have told about the universe has been one of perfect smoothness. This standard story, known as the Lambda Cold Dark Matter model, assumes that if you look at the cosmos on a large enough scale, it looks the same in every direction. It expands evenly, like a balloon being inflated, with no preferred axis or tilt. This idea has worked remarkably well to explain the light left over from the Big Bang and the distribution of galaxies. However, in recent years, astronomers have noticed cracks in this smooth narrative. When they measure how fast the universe is expanding today using nearby stars, they get a different answer than when they calculate that speed based on the ancient light from the early universe. This disagreement, known as the Hubble tension, suggests that our smooth, simple story might be missing a crucial piece of the puzzle.

To address this, a team of researchers has explored a more complex possibility: what if the universe is not perfectly smooth, but slightly lopsided? They investigated a model where the expansion rate differs depending on which direction you look, combined with a new idea about dark energy. In this scenario, the force driving the universe's expansion is not a constant, unchanging value. Instead, it acts like a switch that flipped over time. In the very early universe, this force was negative, pulling things together, but at a specific moment in cosmic history, it switched to positive, pushing the universe apart and causing the acceleration we see today. The researchers wanted to know if adding this directional difference and this switching force could fix the disagreements in our measurements without breaking the parts of the story that already work.

The team, led by Manish Yadav and colleagues, built a mathematical framework that allowed the universe to expand at different rates along three perpendicular directions, while also letting the dark energy change its sign. They then tested this model against the most precise data available from modern astronomy. This included detailed maps of the cosmic microwave background, which is the afterglow of the Big Bang; measurements of the distribution of galaxies from the Dark Energy Spectroscopic Instrument; and observations of distant exploding stars used as cosmic mile markers. By running millions of computer simulations to see which versions of their model best matched the real-world data, they could determine how likely it was that the universe is actually anisotropic, or directionally uneven.

The results were surprisingly precise. The data showed that if the universe is indeed expanding differently in different directions, that difference is incredibly tiny. The researchers calculated that the current level of this directional unevenness is so small that it is effectively zero for all practical purposes, constrained to a value around one part in ten to the power of sixteen. This means that while the model allows for a lopsided universe, the universe we observe is overwhelmingly smooth. The study effectively ruled out any significant, large-scale tilt in the cosmos that could explain the current measurement conflicts. The directional differences are so suppressed that they do not play a major role in the universe's current behavior, even though they might have been more important in the very early moments after the Big Bang.

However, the other part of their model, the switching dark energy, proved to be much more significant. The researchers found that this sign-switching mechanism successfully adjusted the predicted expansion rate of the universe. When they combined data from the early universe with data from nearby supernovae, their model predicted an expansion speed of 72.25 kilometers per second per megaparsec. This value aligns closely with the measurements taken from local stars, which had previously been in conflict with the standard model's prediction of roughly 68 kilometers per second per megaparsec. By incorporating this switching force, the gap between the early and late universe measurements shrank dramatically, reducing the statistical disagreement from a level that was highly unlikely to occur by chance down to a much more manageable level.

The study also looked at how matter clumps together in the universe, a property that has been another source of tension in recent years. The researchers found that their model predicted a level of clumping that matched well with observations from weak gravitational lensing surveys, which measure how light bends around massive objects. This suggests that while the universe might be slightly lopsided, the primary reason for the improved fit to the data is the changing nature of dark energy, not the directional expansion. The team concluded that while the universe appears to be remarkably uniform in its expansion today, the idea that dark energy underwent a fundamental transition from a negative to a positive state offers a compelling way to resolve the long-standing puzzles in cosmology. The model stands as a viable, observationally supported extension to our current understanding, suggesting that the universe's history is more dynamic than the simple, constant expansion we once believed.

Technical Summary: Study of Anisotropy in a Dark Energy Model with Latest Observations

Problem Statement
The standard $\Lambda$ CDM cosmological model, while robust, faces persistent observational tensions, most notably the Hubble tension (the discrepancy between early-universe CMB measurements and late-universe distance-ladder measurements of $H_0$ ) and the $S_8$ tension (discrepancies in matter clustering amplitude). Additionally, the possibility of cosmic expansion anisotropy remains a theoretical avenue for resolving these conflicts. While previous studies have constrained anisotropy parameters ( $\Omega_{\sigma_0}$ ) to extremely low levels ( $O(10^{-14})$ to $O(10^{-23})$ ) and explored sign-switching dark energy models ( $\Lambda_s$ CDM) to alleviate tensions, the combined impact of anisotropic expansion and a dynamical, sign-switching cosmological constant has not been systematically investigated. This study addresses the gap by extending the $\Lambda_s$ CDM framework to include a free anisotropy parameter within a Bianchi type-I spacetime, aiming to assess whether this combined extension can simultaneously constrain anisotropy and alleviate cosmological tensions.

Methodology
The authors constructed a cosmological model based on the Bianchi type-I spacetime, which allows for anisotropic expansion along three orthogonal axes while maintaining spatial homogeneity. The model incorporates a sign-switching cosmological constant ( $\Lambda_s$ ), where the vacuum energy density transitions from negative (Anti-de Sitter-like) in the early universe to positive (de Sitter-like) at later times, governed by a transition redshift $z^\dagger$ . The Friedmann equation was modified to include the shear scalar contribution ( $\sigma^2$ ), representing the anisotropy energy density, which scales as $(1+z)^6$ .

The analysis utilized a comprehensive joint likelihood approach combining three major observational datasets:

Planck 2018 CMB: Including high- $\ell$ and low- $\ell$ temperature and polarization spectra, lensing, and the SimAll likelihood.
DESI DR2 BAO: Utilizing baryon acoustic oscillation measurements from luminous red galaxies, bright galaxies, quasars, and the Lyman- $\alpha$ forest.
PantheonPlus & SH0ES: A compilation of 1,550 Type Ia supernovae calibrated with Cepheid host distances.

Cosmological parameters were constrained using the Markov Chain Monte Carlo (MCMC) technique via the MontePython code interfaced with the CLASS Boltzmann solver. The analysis employed uniform priors for parameters including the baryon density ( $\Omega_b h^2$ ), cold dark matter density ( $\Omega_c h^2$ ), the transition redshift ( $z^\dagger \in [1, 3]$ ), and the present-day anisotropy parameter ( $\Omega_{\sigma_0} \in [0, 0.1]$ ). Model performance was evaluated using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to balance goodness-of-fit against model complexity.

Key Contributions and Results

Anisotropy Constraints: The study places tight constraints on the present-day anisotropy parameter. Across all dataset combinations (CMB alone, CMB+DR2, and CMB+PP&SH0ES), the anisotropy parameter is constrained to $\Omega_{\sigma_0} \sim 10^{-16}$ at the 95% confidence level. Specifically, the CMB-only dataset yields an upper limit of $\Omega_{\sigma_0} < 0.74 \times 10^{-16}$ . The results indicate that while anisotropy is non-vanishing, it is highly suppressed in the current epoch, consistent with the rapid dilution of shear energy ( $\propto a^{-6}$ ) relative to radiation and matter.
Transition Redshift ( $z^\dagger$ ): The transition redshift, marking the switch from negative to positive dark energy, is well-constrained when BAO data is excluded. The CMB+PP&SH0ES combination yields a mean value of $z^\dagger = 1.74^{+0.11}_{-0.18}$ . The inclusion of anisotropy was found to have only a minor effect on the preferred range of $z^\dagger$ , suggesting the sign-switching mechanism is robust even with small anisotropic contributions.
Hubble Tension Alleviation: The extended $\Lambda_s$ CDM+ $\Omega_{\sigma_0}$ model significantly impacts the estimation of the Hubble constant. When combining CMB with PantheonPlus and SH0ES data, the model yields $H_0 = 72.25 \pm 0.90$ km s $^{-1}$ Mpc $^{-1}$ , which strongly favors the local SH0ES calibration. This result reduces the statistical significance of the Hubble tension from the standard $\sim 5\sigma$ (in $\Lambda$ CDM) to approximately the $3.7\sigma$ level.
$S_8$ Parameter: The model predicts $S_8$ values consistent with recent weak-lensing observations (e.g., KiDS-Legacy). The analysis indicates that the inclusion of anisotropy does not lead to significant improvements or noticeable changes in $S_8$ constraints compared to the isotropic $\Lambda_s$ CDM model, implying anisotropy has a negligible effect on matter clustering amplitude within this framework.
Model Comparison: Statistical model selection using AIC and BIC reveals that the $\Lambda_s$ CDM+ $\Omega_{\sigma_0}$ model receives very strong observational support relative to the standard $\Lambda$ CDM model when the CMB and supernova datasets are combined. While the BIC penalizes the additional parameters, the substantial improvement in fit for the sign-switching models results in negative $\Delta$ AIC and $\Delta$ BIC values (indicating preference) for the CMB+PP&SH0ES combination.

Significance and Claims
The paper claims that the proposed $\Lambda_s$ CDM+ $\Omega_{\sigma_0}$ framework offers a consistent and observationally viable extension to the standard cosmological model. The primary significance lies in demonstrating that a sign-switching dark energy model, even when extended to include anisotropic expansion, can effectively alleviate the Hubble tension without introducing significant discrepancies in other cosmological parameters like $S_8$ .

The authors modestly conclude that the anisotropic contribution remains subdominant and tightly constrained, with the primary driver of the improved fit being the sign-switching mechanism rather than the anisotropy itself. The study asserts that the combined model preserves the successful predictions of $\Lambda$ CDM at late times while providing a potential pathway to resolve current cosmological tensions. The findings suggest that future high-precision surveys will be necessary to further test the viability of this framework and clarify the specific role of anisotropic expansion in cosmic evolution.

Technical Summary: Study of Anisotropy in a Dark Energy Model with Latest Observations

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