🔭 astrophysics

Constraints on the gravitational potential from DESI DR2 BAO and its implications for the local void scenario

This paper investigates whether a local void, proposed as a solution to the Hubble tension, is constrained by DESI DR2 BAO and other high-redshift datasets, finding that while the data slightly favor a standard universe, a void large enough to resolve the tension remains statistically viable despite its novel effects on the CMB and BAO scale.

Original authors: Indranil Banik, José Antonio Nájera, Harry Desmond

Published 2026-06-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Indranil Banik, José Antonio Nájera, Harry Desmond

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

The Big Problem: The Universe's Speedometer is Broken

Imagine the universe is a car driving away from us. For over a century, we've known it's speeding up. But there is a major disagreement among the mechanics (cosmologists) about exactly how fast it is going right now. This is called the "Hubble Tension."

Mechanic A (The Early Universe Team): They look at the "baby photos" of the universe (the Cosmic Microwave Background, or CMB). Based on how the universe started, they calculate the speed should be about 67 km/s per megaparsec.
Mechanic B (The Local Team): They look at the "current traffic" (nearby stars and galaxies). They measure the speed to be about 73 km/s per megaparsec.

These two numbers don't match. It's like one mechanic says the car is doing 60 mph, and the other says it's doing 70 mph, but they are both looking at the same car.

The Suspect: A Giant "Empty" Neighborhood

One theory suggests the problem isn't with the speedometer, but with where we are sitting. The theory proposes that our solar system is located inside a massive, giant bubble of empty space—a Local Void.

Think of it like this:

Standard Theory: The universe is a flat, smooth highway. Everyone sees the same speed.
Void Theory: We are sitting in a giant crater (the void). Because we are at the bottom of a "gravity hill," light coming from distant galaxies has to climb out of this hole to reach us. As it climbs, it loses energy and gets stretched (redshifted). This makes the galaxies look like they are moving away faster than they actually are.

If this is true, our local measurement of 73 is "fake" because of the hill we are standing on, and the real speed is actually the 67 predicted by the baby photos.

The Investigation: Checking the Evidence

The authors of this paper wanted to test if this "Local Void" theory holds up when we look at data from far away (high redshift), not just nearby.

They used a new, very precise dataset called DESI DR2, which acts like a giant ruler (the Baryon Acoustic Oscillation or BAO) to measure distances in the universe. They also checked data from the Big Bang (CMB) and the formation of elements (BBN).

The Twist:
The authors realized that if we are in a gravity hill, it doesn't just mess up nearby measurements. It creates "spillover" effects that change how we see the entire universe, even far away.

The Hotter CMB: If we are on a gravity hill, the light from the early universe (the CMB) has to climb out to reach us. This makes the universe look slightly hotter to us than it really is.
The Shrinking Ruler: Because the universe looks hotter, the "standard ruler" (BAO) we use to measure distances would actually be slightly smaller than we thought.

The Experiment: Putting the Theory to the Test

The team ran a simulation where they allowed the "height" of this gravity hill (called $z_0$ ) to vary.

The Prediction: Previous studies suggested the hill should be about 0.84% high to explain the speed difference.
The Test: They fed all the new, high-precision data (DESI, CMB, etc.) into their computer models to see what the actual height of the hill should be.

The Results: A "Maybe" Verdict

Here is what they found:

The Best Fit is Still "Flat": When they let the data speak for itself, the most likely answer is that there is no hill at all ( $z_0 = 0$ ). The standard model (a flat universe) fits the data best.
But the "Hill" isn't Ruled Out: However, the data is not precise enough to completely kill the idea. The "hill" could be as high as 0.84% (the value needed to solve the speedometer problem), and the data would still look okay. It's not a perfect fit, but it's not a terrible one either.
The "Anomaly" Gets Smaller: There is a known glitch in the standard model where the "baby photos" and the "current traffic" disagree on the shape of the universe's expansion.
- In the standard model, this disagreement is a 2.81-sigma problem (a significant glitch).
- If you assume the Local Void exists ( $z_0 = 0.84\%$ ), that glitch shrinks to 2.39-sigma.
- Analogy: It's like the standard model has a 28% chance of being wrong, but the Void model reduces that to a 24% chance. It doesn't fix the problem entirely, but it makes it look a bit less suspicious.

The Conclusion

The paper concludes that we cannot yet prove or disprove the Local Void theory.

The data prefers the standard "flat" universe.
However, the "Local Void" theory is still alive. It fits the new, high-precision data almost as well as the standard model does.
If the Local Void is real, it would mean that the "spillover" effects (like the hotter CMB and smaller ruler) are happening, but they are subtle enough that our current telescopes can't definitively say "No, that's not it."

In short: The universe might be a flat highway, or it might be a giant crater. Our current measurements are too fuzzy to tell the difference for sure, but the "crater" theory is still a valid suspect that hasn't been caught yet.

Technical Summary: Constraints on the Gravitational Potential from DESI DR2 BAO and its Implications for the Local Void Scenario

Problem Statement
The paper addresses the "Hubble tension," a significant discrepancy between the local expansion rate ( $H_0 \approx 73.5$ km/s/Mpc) and the value inferred from the Cosmic Microwave Background (CMB) under the standard $\Lambda$ CDM cosmology ( $H_0 \approx 67.2$ km/s/Mpc). One proposed resolution is the "local void" scenario, suggesting we reside in a large underdensity (the Keenan-Barger-Cowie or KBC void). In this model, the observed local Hubble constant is inflated by two mechanisms: peculiar outflow velocities and Gravitational Redshift (GR) as photons climb out of the local potential hill. While peculiar velocities dominate at low redshift, GR becomes the dominant effect at higher redshifts ( $z \gtrsim 0.5$ ), contributing a fixed additional redshift term $z_0$ . Previous work (Haslbauer, Banik & Kroupa 2020, hereafter HBK20) suggested a void capable of solving the Hubble tension would imply $z_0 \approx 0.84\%$ . However, this model predicts "spillover" effects at high redshift, including a hotter CMB and a reduced sound horizon ( $r_d$ ), which had not been rigorously tested against the latest high-precision data, specifically the Baryon Acoustic Oscillation (BAO) measurements from DESI Data Release 2 (DR2).

Methodology
The authors test the local void hypothesis by introducing a parameter $z_0$ representing the dimensionless height of the local gravitational potential hill. They approximate the observed redshift $z$ as $1+z = (1+z_c)(1+z_0)$ , where $z_c$ is the cosmological redshift. This approximation neglects peculiar velocities, which is valid at $z \gtrsim 0.5$ where sources lie beyond the void.

The analysis utilizes a comprehensive dataset including:

Big Bang Nucleosynthesis (BBN): Constraints on the baryon density.
Cosmic Microwave Background (CMB): Compressed likelihoods from SPT-3G, Planck, and ACT, accounting for the effect of a hotter CMB ( $T_{CMB} = T_{FIRAS}(1+z_0)$ ) on the physical baryon density ( $\omega_b$ ) and matter density ( $\omega_{bc}$ ).
Cosmic Chronometers (CC): Measurements of the expansion rate $H(z)$ .
BAO: 13 measurements from DESI DR2, analyzed in two redshift ranges: a "nominal" range ( $z > 0.5$ ) and an "extended" range ( $z > 0.29$ ).

The authors perform Markov Chain Monte Carlo (MCMC) analyses using the dynesty nested sampling algorithm. They vary cosmological parameters ( $\omega_b, \omega_{bc}, H_0, z_0$ ) and calculate the Bayesian evidence. Crucially, they recalculate the sound horizon $r_d$ and recombination temperature $T_*$ for each $z_0$ value using the CLASS code, acknowledging that a hotter CMB implies less expansion since decoupling, thereby altering the calibration of BAO and CMB observables.

Key Contributions

Refined High-Redshift Constraints: The paper provides the first detailed constraints on $z_0$ using DESI DR2 BAO data, moving beyond previous studies that fixed cosmological parameters to Planck best-fits without considering the self-consistent impact of $z_0$ on the sound horizon and CMB temperature.
Quantification of "Spillover" Effects: The authors explicitly model how a local void affects high-redshift observables, demonstrating that a hotter CMB leads to a reduced $r_d$ and a reduced product $H_0 r_d$ , which are tightly constrained by BAO.
BAO Anomaly Analysis: The study quantifies the "BAO anomaly" (the tension between BAO and non-BAO datasets in the $(H_0 r_d, \Omega_m)$ parameter space) using the Maximum of Data and Parameter Space (MDPS) tension metric. They compare the performance of the local void model against standard $\Lambda$ CDM and phenomenological background solutions.

Results

Constraints on $z_0$ : Combining BBN, CMB, BAO, and CC data, the authors find $z_0 = -0.4 \pm 0.9\%$ for the nominal range ( $z > 0.5$ ) and $z_0 = 0.0^{+0.6}_{-0.7}\%$ for the extended range ( $z > 0.29$ ). While the data slightly prefer $z_0 = 0$ (standard $\Lambda$ CDM), the value $z_0 = 0.84\%$ (predicted by HBK20) remains within the $2\sigma$ confidence interval.
Model Fit: The best-fitting model with $z_0 = 0.84\%$ fits the data almost as well as $\Lambda$ CDM, with a difference in chi-squared ( $\Delta \chi^2$ ) of less than 2. The Bayesian evidence slightly disfavors the addition of $z_0$ as a free parameter, but the difference is small (loss of $\sim 0.5$ nats for fixed $z_0=0.84\%$ ).
BAO Tension: In the standard $(H_0 r_d, \Omega_m)$ parameter space, $\Lambda$ CDM faces a tension of $2.81\sigma$ when compared to non-BAO datasets (using the extended redshift range). Fixing $z_0 = 0.84\%$ reduces this tension to $2.39\sigma$ , bringing it within the 99% credible region. This reduction occurs because the local void model shifts the preferred parameter regions for BAO and non-BAO datasets, partially reconciling them.
Data Space vs. Parameter Space: While the void model slightly worsens the fit in "data space" (direct prediction of DESI measurements), it improves the consistency in "parameter space." The MDPS tension (the maximum of the two) is reduced from $2.81\sigma$ in $\Lambda$ CDM to $2.39\sigma$ in the void model.

Significance and Claims
The paper concludes that a local void large enough to solve the Hubble tension (implying $z_0 \approx 0.84\%$ ) cannot be ruled out by current high-redshift datasets, despite the model's novel impacts on the CMB temperature and sound horizon. While the data slightly prefer the standard $\Lambda$ CDM value of $z_0=0$ , the void model with $z_0=0.84\%$ provides an acceptable fit to all datasets (BBN, CMB, BAO, CC) and notably alleviates the parameter space tension between BAO and other high-redshift probes.

The authors emphasize that their results do not confirm the local void scenario but demonstrate its viability against high-precision constraints that were previously thought to potentially exclude it. They suggest that the "BAO anomaly" observed in $\Lambda$ CDM may be partially mitigated by the local void hypothesis, and that future data releases (potentially revising the $z=0.7$ BAO measurement) could further align the inferred $z_0$ with the $0.84\%$ prediction. The study motivates more detailed low-redshift modeling that includes outflows to fully assess the void scenario's ability to resolve the Hubble tension.