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Cosmographic constraints on a Gödel-type rotating universe

Using a cosmographic analysis of Pantheon+ Type Ia supernovae data, this study finds a mild but statistically significant preference for a Gödel-type rotating universe over the standard $\Lambda$ CDM model at intermediate redshifts, suggesting that global cosmic rotation may influence the late-time expansion history.

Original authors: Anshul Verma, Pavan K. Aluri, David F. Mota, Yuri N. Obukhov

Published 2026-06-30

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CC BY 4.0

Original authors: Anshul Verma, Pavan K. Aluri, David F. Mota, Yuri N. Obukhov

Original paper licensed under CC BY 4.0 (http://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

Imagine the universe as a giant, expanding balloon. For decades, the standard story (called the ΛCDM model) has been that this balloon is inflating perfectly evenly in all directions, like a smooth, round sphere growing in a quiet room.

But what if the universe isn't just expanding? What if it's also spinning?

This paper asks that exact question. The authors, a team of physicists from India, Norway, and Russia, investigated whether our universe has a global "spin," similar to how a figure skater spins while gliding across the ice. They used a specific mathematical model called a Gödel-type universe, which allows for both expansion and rotation, to see if the data supports this spinning idea.

Here is a breakdown of their findings using simple analogies:

1. The Detective Work: Looking at "Cosmic Beacons"

To test if the universe is spinning, the team acted like cosmic detectives. They used Type Ia supernovae as their clues. Think of these supernovae as "standard lightbulbs" scattered across the universe. Because we know exactly how bright they should be, we can tell how far away they are by how dim they look to us.

They looked at 1,701 of these lightbulbs (from a dataset called Pantheon+) and checked their brightness against their distance (redshift). If the universe were perfectly smooth and non-spinning, the light from these bulbs would follow a very specific, predictable pattern. If the universe were spinning, the light would arrive slightly differently depending on which direction you looked, much like how a spinning merry-go-round might make a thrown ball curve slightly differently depending on where you stand.

2. The Main Discovery: A "Mild" Spin

The team found some interesting hints that the universe might indeed be rotating, but it's a subtle effect.

The Spin Rate: They calculated a "spin parameter" (called $\Omega_0$ ). For the closest group of supernovae (up to a certain distance), the data suggested a spin value of about 0.29. This isn't a wild, chaotic spin; it's more like a slow, steady turn.
The Direction: If the universe is spinning, it has to spin around an axis, just like Earth spins around the North and South Poles. The team pinpointed this cosmic axis to a specific spot in the sky (near the constellation Sagittarius). Interestingly, this direction aligns somewhat with other "weird" directions scientists have noticed in the cosmic microwave background (the afterglow of the Big Bang) and radio waves from distant galaxies.

3. The "Hubble Constant" (The Expansion Speed)

One of the biggest mysteries in physics right now is the "Hubble Tension"—a disagreement between different ways of measuring how fast the universe is expanding.

The Finding: The authors found that even with this new spinning model, the calculated expansion speed (the Hubble constant) stayed very stable at 0.73.
The Analogy: Imagine a car driving down a highway. Whether the car is just driving straight or driving straight while also turning the steering wheel slightly, the speedometer still reads the same speed. The "spin" didn't break the speedometer; it just added a new layer of complexity to the journey.

4. The "Deceleration" Puzzle

The team also looked at whether the universe is speeding up or slowing down its expansion (the deceleration parameter, $q_0$ ).

The Twist: In the standard model, the universe is accelerating (speeding up). In their spinning model, the data suggested the universe was barely accelerating or even slightly slowing down at very close distances, before settling into a pattern closer to the standard model at farther distances.
The Takeaway: This suggests that if the universe is spinning, that spin might be having a tiny, local effect on how we perceive the expansion of space nearby, but it fades away as we look further out.

5. Which Model Wins? The "Cost-Benefit" Analysis

The authors compared their "Spinning Universe" model against the standard "Non-Spinning" model using a statistical tool called the Akaike Information Criterion (AIC). Think of AIC as a judge that asks: "Is the extra complexity of adding a spin worth the better fit to the data?"

The Verdict: For the closest supernovae, the two models were almost equal. But for the intermediate-distance supernovae (the middle ground), the Spinning Model won. The data was about 3 to 10 times more likely to come from a spinning universe than a non-spinning one in these specific ranges.

6. The Caveat: Don't Pop the Champagne Yet

The authors are very careful not to claim they have proven the universe is spinning.

The Limitation: Their analysis used a "Taylor expansion," which is like looking at a curve through a small window. It works well for nearby objects but might not tell the whole story for the entire universe.
The Conclusion: The results are "intriguing" and "statistically significant" for the middle distances, suggesting that cosmic rotation might be a real thing that influences how the universe expands. However, they need more data and more advanced math (beyond their current "window") to confirm if this is a true physical reality or just a statistical fluke.

Summary

In short, the paper suggests that the universe might not be a perfectly smooth, expanding balloon. It might be a spinning balloon. While the spin is gentle and doesn't change the overall speed of expansion, it appears to leave a detectable fingerprint in the light of distant supernovae, particularly at intermediate distances. The standard "non-spinning" model is still a strong contender, but the "spinning" model fits the data slightly better in certain regions, warranting further investigation.

Technical Summary: Cosmographic Constraints on a Gödel-type Rotating Universe

Problem Statement
The standard cosmological model ( $\Lambda$ CDM) assumes the Cosmological Principle, positing a homogeneous and isotropic universe. However, rotation is a ubiquitous phenomenon in astrophysical systems, from asteroids to galactic centers. This raises the question of whether the universe itself possesses a global rotation. While previous studies have investigated cosmic rotation using Bianchi models and CMB data, results have been inconclusive, often failing to separate vorticity from shear or lacking statistical significance. Furthermore, the standard model faces tensions, such as the Hubble tension, and exhibits various anomalies (e.g., CMB preferred axes) that rotating cosmological models could potentially address. This study investigates the possibility of global cosmic rotation by constraining a Gödel-type rotating cosmological model using Type Ia supernova (SNIa) data.

Methodology
The authors employ a cosmographic analysis using the Pantheon+ dataset, which comprises 1701 light curves from approximately 1550 unique spectroscopically confirmed SNIa. The analysis focuses on low-redshift data ( $Z \leq 0.5$ ) to remain within the validity of a Taylor-expanded magnitude-redshift relation.

Theoretical Framework: The study utilizes a non-stationary, expanding Gödel-type metric (Eq. 2) that is free of closed time-like curves (CTCs). This metric incorporates a time-dependent scale factor $R(t)$ , rotation, and expansion. The global rotation parameter $\omega$ is defined along the $z$ -axis (anisotropy axis).
Observational Relation: Using the Kristian-Sachs formalism, the authors derive a Taylor-expanded relation between the apparent magnitude ( $m$ ) and redshift ( $Z$ ) up to linear order. This relation (Eq. 9) includes terms for the Hubble parameter ( $h_0$ ), deceleration parameter ( $q_0$ ), and a dimensionless rotation parameter ( $\Omega_0$ ), as well as the direction of the anisotropy axis $(R_a, D_a)$ .
Statistical Analysis: A Markov Chain Monte Carlo (MCMC) likelihood analysis is performed to constrain the model parameters: $\Xi = \{h_0, \Omega_0, q_0, \tilde{\rho}, (R_a, D_a), M_0, \alpha, \beta, \gamma\}$ . The analysis minimizes the $\chi^2$ function comparing theoretical distance moduli ( $\mu_{th}$ ) with observed values ( $\mu_{obs}$ ), utilizing the full covariance matrix (statistical and systematic) provided by the Pantheon+ collaboration.
Redshift Binning: Parameters are estimated across five redshift bins ( $Z \leq 0.1$ to $Z \leq 0.5$ ) to track the evolution of constraints.
Model Comparison: The rotating Gödel-type model is compared against the standard flat $\Lambda$ CDM model using the Akaike Information Criterion (AIC) to penalize model complexity and assess relative probabilities.

Key Results

Hubble Constant ( $h_0$ ): The inferred Hubble constant remains stable across all redshift bins for both the Gödel-type and $\Lambda$ CDM models, with $h_0 \approx 0.73$ . This aligns with SH0ES determinations and suggests that the inclusion of rotation does not significantly alter the local expansion rate.
Deceleration Parameter ( $q_0$ ): In the Gödel-type model, $q_0$ trends from near-zero ( $0.01 \pm 0.32$ ) at $Z \leq 0.1$ to mildly negative values ( $-0.089^{+0.055}_{-0.039}$ ) at $Z \leq 0.4$ . These values are less negative than those found in the standard $\Lambda$ CDM analysis of the same data subsets, suggesting a potential local effect of rotation on expansion dynamics.
Rotation Parameter ( $\Omega_0$ ): The dimensionless rotation parameter shows a mild but consistent preference for non-zero values. It peaks at $\Omega_0 = 0.29^{+0.21}_{-0.15}$ for the $Z \leq 0.2$ bin and decreases to $0.120^{+0.078}_{-0.046}$ for $Z \leq 0.5$ . The ratio $\Omega_0/h_0$ (rotation vs. expansion strength) follows a similar trend, peaking at $\approx 0.40$ for $Z \leq 0.2$ and diminishing at higher redshifts.
Anisotropy Axis: The inferred axis of rotation is consistent across bins, centered around equatorial coordinates $(R_a, D_a) \approx (243^\circ, -49^\circ)$ . This aligns broadly with other reported preferred axes in cosmological data.
Model Comparison (AIC): The AIC analysis indicates a statistically significant preference for the rotating Gödel-type model over the standard $\Lambda$ CDM model at intermediate redshifts. Specifically, for $Z \leq 0.3$ , $0.4$, and $0.5$, the rotating model is found to be approximately 9.9, 4.7, and 6.9 times more probable, respectively, than the reference $\Lambda$ CDM model.

Significance and Claims
The paper claims that its findings suggest cosmic rotation, if present, may influence the late-time expansion history of the universe, particularly at intermediate redshifts. The preference for the rotating model in the AIC comparison is described as "unexpected and interesting," implying that kinematic effects from rotation could play a non-negligible role.

However, the authors maintain a modest tone regarding the definitive nature of these results. They explicitly state that the significance of this preference depends on the robustness of the cosmographic expansion and the impact of potential systematics. The paper concludes that while the results warrant further investigation, they do not yet constitute a definitive resolution to cosmological tensions or a proof of global rotation. The authors suggest that future observations from surveys like Euclid and JWST, along with analyses beyond the cosmographic regime (e.g., solving the full luminosity-redshift relation), are necessary to determine whether the observed preference is a genuine physical effect or a statistical anomaly.