🔭 astrophysics

The local void model for the Hubble and BAO tensions

This paper proposes that the Hubble and BAO tensions arise from the observer residing in a large local underdensity (the KBC void), which induces gravitational outflows that inflate low-redshift recession velocities and mimics a higher local Hubble constant while remaining consistent with CMB predictions at higher redshifts.

Original authors: Indranil Banik, Harry Desmond, Vasileios Kalaitzidis, Sergij Mazurenko

Published 2026-02-17

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CC BY 4.0

Original authors: Indranil Banik, Harry Desmond, Vasileios Kalaitzidis, Sergij Mazurenko

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 Great Cosmic Speedometer Glitch: A Story of a Local "Empty" Neighborhood

Imagine the universe as a giant, expanding balloon. For decades, cosmologists have been trying to measure exactly how fast this balloon is inflating. This rate is called the Hubble Constant.

Here is the problem: We have two very different speedometers, and they aren't agreeing.

The "Baby Picture" Speedometer: If we look at the Cosmic Microwave Background (CMB)—which is essentially a baby picture of the universe taken 13.8 billion years ago—and use our standard rules of physics (called the ΛCDM model) to predict how fast the universe should be expanding today, we get a speed of about 67 km/s/Mpc.
The "Local Neighborhood" Speedometer: If we look at nearby galaxies right now and measure how fast they are zooming away from us, we get a speed of about 73–74 km/s/Mpc.

That's a 9% difference. In the world of physics, that's not a rounding error; it's a massive crisis. It's like one group of scientists saying a car is doing 60 mph, and another group, looking at the same car, saying it's doing 66 mph.

The Proposed Solution: We Live in a "Cosmic Desert"

This paper, written by Indranil Banik and colleagues, suggests a radical idea: The universe isn't perfectly uniform, and we happen to be living in a giant, empty bubble.

The Analogy: The Hiking Trail

Imagine you are hiking up a mountain.

The Standard View (ΛCDM): The mountain is a smooth, uniform slope. If you measure the steepness at the bottom, it should match the steepness at the top.
The "Void" View: Imagine you are standing in a giant, bowl-shaped depression at the bottom of the mountain. The ground around you is lower than the ground further out.

Because you are in this "bowl" (a Local Void), gravity is pulling you outward toward the denser edges of the universe. This creates two effects that mess up your speedometer:

The Outward Push (Peculiar Velocity): Just like water rushing out of a bathtub drain, galaxies near you are being pushed away from the center of this empty bubble. This adds extra speed to their movement.
The Gravity Hill (Gravitational Redshift): Because you are in a low-density area (a "hill" of low gravity compared to the dense universe outside), light coming from distant galaxies has to climb up out of your local gravity well to reach you. This stretches the light, making the galaxies look like they are moving away faster than they actually are.

The Result: When we measure the speed of nearby galaxies, we are measuring the "true" expansion of the universe PLUS this extra "push" from our local empty bubble. This makes the local speedometer read 73, while the "baby picture" (which sees the universe as a whole, averaging out the bubble) still reads 67.

Why This Makes Sense of the "BAO Anomaly"

The paper also tackles a second mystery called the BAO Tension.

What is BAO? Think of the early universe as a giant drum. When it was very young, sound waves rippled through the hot gas. When the universe cooled, these waves froze in place, creating a "standard ruler" in the distribution of galaxies. We know exactly how big this ruler is.
The Problem: When we measure this ruler in the distant past (high redshift), it fits our "Baby Picture" perfectly. But when we measure it in the nearby universe (low redshift), the ruler seems too small. It looks like the galaxies are closer together than they should be.

The Void Explanation:
If we are in a giant empty bubble, the space around us is expanding faster than the rest of the universe. This extra expansion squishes the "standard ruler" in our local neighborhood. It makes the distance to a galaxy look shorter than it really is.

The authors show that if you take their "Local Void" model and run the numbers, it perfectly predicts this shrinking ruler effect. It's like the model was a crystal ball that predicted the BAO anomaly years before the data confirmed it.

How Do We Know We Are in a Bubble?

The paper points to evidence from galaxy counts. If you look at the night sky in infrared light, you notice that there are fewer galaxies nearby than there are a bit further away. It's as if you are standing in a clearing in a forest, and the trees (galaxies) only start appearing once you walk a few hundred million light-years out. This structure is known as the KBC Void.

The Future: How to Prove It

The authors admit that proving we live in a bubble is hard, but they suggest some clever ways to test it:

Fast Radio Bursts (FRBs): These are mysterious radio signals from deep space. They travel through the "fog" of free electrons in space. If we are in a bubble, the fog is thinner nearby. By measuring how much the signal slows down, we can map the density of the universe. If the fog is thinner than expected, it confirms the bubble.
Redshift Drift: Imagine watching a galaxy for 10 years. In a normal universe, its speed changes very slowly. But if we are in a bubble, the "push" from the bubble might change in a specific way over time. Future telescopes might be able to see this tiny change in real-time.
The Kinematic Sunyaev-Zel'dovich Effect: This is a fancy way of measuring how hot gas in galaxy clusters is moving relative to the cosmic background. If the whole cluster is being pushed outward by our local void, we should see a specific "wind" pattern.

The Bottom Line

The universe is currently in a "crisis" because our local measurements don't match our global predictions. This paper argues that the crisis isn't because our physics is wrong, but because we are in a special, empty neighborhood.

Just as a person standing in a valley might think the surrounding hills are steeper than they actually are, we might be misinterpreting the speed of the universe because we are sitting in a giant cosmic void. If this is true, it solves the Hubble tension, explains the BAO anomaly, and suggests that gravity might behave slightly differently on the largest scales than we thought.

It's a reminder that in science, sometimes the answer isn't that the rules are broken, but that we were standing in the wrong place to see the whole picture.

1. The Problem: The Hubble and BAO Tensions

The paper addresses the persistent Hubble Tension, a statistically significant ( $>7\sigma$ ) discrepancy between the Hubble constant ( $H_0$ ) inferred from the Cosmic Microwave Background (CMB) under the $\Lambda$ CDM model ( $H_0^{CMB} \approx 67.24$ km/s/Mpc) and the locally measured value ( $H_0^{local} \approx 73.5$ km/s/Mpc).

Key characteristics of the problem identified in the paper:

Redshift Dependence: The tension is driven almost exclusively by data at very low redshifts ( $z < 0.15$ ). Intermediate redshift probes ( $z \gtrsim 0.2$ ) and CMB data remain consistent with each other under $\Lambda$ CDM.
The BAO Anomaly: There is a growing anomaly in Baryon Acoustic Oscillation (BAO) measurements at low redshift ( $z \lesssim 1$ ). The observed BAO distance scale ( $D_V$ ) is smaller than predicted by $\Lambda$ CDM calibrated with the CMB, quantified by a deviation parameter $\alpha_{iso} < 1$ . This discrepancy reaches $\sim 3.8\sigma$ when combining all available low- $z$ BAO data.
The Local Void Hypothesis: The authors propose that the observed high local $H_0$ is not due to a fundamental change in the background expansion rate of the universe, but rather an artifact of the observer residing within a large local underdensity (the Keenan-Barger-Cowie or KBC void). In such a void, gravitational effects (peculiar velocities and gravitational redshift) inflate the locally inferred recession velocity ($cz'$) relative to the true background expansion rate.

2. Methodology

The authors employ a combination of semi-analytic modeling, observational data synthesis, and theoretical reconstruction to test the local void hypothesis.

Semi-Analytic Void Modeling:
- They utilize the model developed by Haslbauer et al. (2020), which simulates a spherical void evolving from $z=9$ to $z=0$ .
- The model assumes a background Planck cosmology but modifies gravity on large scales ( $\gtrsim 100$ Mpc) using a factor inspired by Milgromian dynamics (MOND) to allow for the rapid growth of the KBC void, which is otherwise impossible in standard $\Lambda$ CDM.
- Three initial underdensity profiles are tested: Exponential, Gaussian, and Maxwell-Boltzmann.
Redshift Calculation:
- The observed redshift ( $z$ $z$ ) is modeled as a combination of three components (Equation 5):
  1. Cosmic Expansion: The standard $1/a(t)$ term.
  2. Doppler Shift: Caused by coherent outward peculiar velocities ( $v_{int}$ ) induced by the void's mass deficit.
  3. Gravitational Redshift (GR): Caused by the observer being at a higher gravitational potential relative to distant sources.
- The authors demonstrate that GR is the dominant contributor to the redshift anomaly at the distances probed by BAO, while Doppler effects dominate at very low $z$ .
Data Synthesis:
- BAO Data: They compare model predictions against 20 years of BAO measurements (including DESI DR2), specifically analyzing the ratio $\alpha_{iso} = (D_V/r_d) / (D_V/r_d)_{fid}$ .
- $H_0(z)$ Reconstruction: They analyze recent reconstructions of the expansion history using uncalibrated BAO and Type Ia Supernovae (SNe Ia) to see if the data supports a transition from a high local $H_0$ to the CMB value at higher $z$ .
- Future Probes: They evaluate the potential of Fast Radio Bursts (FRBs), kinematic Sunyaev-Zel'dovich (kSZ) effect, and redshift drift experiments to distinguish between local void and background expansion solutions.

3. Key Contributions

Unified Explanation of Hubble and BAO Tensions: The paper argues that the Hubble tension and the low- $z$ BAO anomaly are two sides of the same coin. A local void naturally predicts that distances to a given redshift are smaller than expected ( $\alpha_{iso} < 1$ ) at low $z$ , while converging to the standard $\Lambda$ CDM prediction at high $z$ .
A Priori Prediction of BAO Data: The authors highlight that the void model parameters were constrained only using local $cz'$ and galaxy number counts (prior to 2020). When these fixed parameters are used to predict BAO data, the model matches the observed $\alpha_{iso}$ trend remarkably well, reducing the tension from $3.8\sigma$ (in $\Lambda$ CDM) to $1.1\text{--}1.3\sigma$ .
Distinction from Background Solutions: The paper provides a framework to distinguish between a "local void" solution (inhomogeneous) and a "background" solution (modified Friedmann equations). It emphasizes that while both can fit $H_0(z)$ trends, only the void model naturally explains the existence of the KBC void and the specific anisotropic signatures expected in peculiar velocities.
Quantification of GR vs. Doppler: The study explicitly quantifies the role of Gravitational Redshift, showing it is crucial for explaining the BAO anomaly at $z > 0.1$ , whereas Doppler shifts alone are insufficient.

4. Results

BAO Fit: The local void models (with background Planck cosmology) successfully reproduce the observed decline in $\alpha_{iso}$ at $z < 1$ . The $\chi^2$ for the void models is significantly lower than for the homogeneous Planck cosmology when fitting the full BAO dataset.
$H_0(z)$ Evolution: The predicted $H_0(z)$ curve for the void model shows a rapid transition from the local value ( $\sim 73.5$ km/s/Mpc) to the CMB value ( $\sim 67.2$ km/s/Mpc) by $z \approx 0.2$ . This aligns with recent empirical reconstructions (e.g., Jia et al. 2025b) that find no Hubble tension at $z \gtrsim 0.2$ .
KBC Void Consistency: The model requires a void with a radius of $\sim 300$ Mpc and a density contrast of $\sim 20\text{--}30\%$ (after correcting for redshift-space distortions). This is consistent with multi-wavelength galaxy number counts (optical, IR, radio, X-ray) which suggest a local underdensity.
Future Probes:
- FRBs: The paper predicts that FRBs will yield a higher $H_0$ ( $\sim 76$ km/s/Mpc) than standard candles because their distance estimation (via Dispersion Measure) assumes homogeneity, leading to an underestimation of distance in a void, which in turn inflates the derived $H_0$ .
- kSZ Effect: The model predicts large coherent bulk flows ( $\sim 600$ km/s) which are currently marginally consistent with observations but could be confirmed with better data.
- Redshift Drift: Distinguishing the void model from background solutions via redshift drift ( $\dot{z}$ ) will require velocity precision of a few mm/s over a decade, which is currently beyond reach but feasible with future instruments.

5. Significance

Paradigm Shift: If validated, this model suggests that the Hubble tension does not require new physics in the early universe (e.g., early dark energy) or a modification of the Friedmann equations at the background level. Instead, it points to a breakdown of the Cosmological Principle (homogeneity) on scales of $\sim 300$ Mpc.
Gravity on Large Scales: The existence of such a large, deep void implies that structure growth on scales $\gtrsim 100$ Mpc is faster than predicted by $\Lambda$ CDM, potentially indicating a modification to gravity (e.g., MOND-like effects) on these scales.
Resolution of Multiple Anomalies: The model offers a self-consistent explanation for the Hubble tension, the BAO anomaly, the KBC void, and the CMB Cold Spot, linking them as causal consequences of a single local underdensity.
Future Direction: The paper outlines a clear path for falsification or confirmation using FRBs, improved bulk flow measurements, and redshift drift, moving the debate from statistical tension to direct physical testing of the local density field.

In conclusion, Banik et al. present a compelling case that the Hubble and BAO tensions are observational artifacts caused by our location within a massive local void, driven by enhanced gravitational growth of structure, rather than a failure of the standard cosmological model's background expansion history.