⚛️ general relativity

Cosmological Constraints on the DGP Model in light of DESI DR2 2025 Data

Using the latest DESI DR2 BAO data combined with other cosmological probes, this study finds that both flat and non-flat DGP models are strongly disfavored and fail to resolve the Hubble tension, as they predict a significantly lower Hubble constant than the Planck $\Lambda$ CDM value.

Original authors: Xinyi Dai, Yupeng Yang, Yicheng Wang

Published 2026-07-13

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Xinyi Dai, Yupeng Yang, Yicheng Wang

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, scientists have been trying to figure out exactly how fast this balloon is inflating and what invisible force is blowing air into it. The current "gold standard" theory, called $\Lambda$ CDM, suggests the balloon is being pushed by a mysterious, unchanging energy called the cosmological constant. But there's a problem: when we measure the balloon's speed using different tools, we get different answers. This is the famous "Hubble Tension."

Enter the DGP model, a bold new idea proposed by physicists Dvali, Gabadadze, and Porrati. Instead of an invisible energy pushing the balloon, DGP suggests our entire 4D universe is just a thin sheet (a "brane") floating in a giant, 5D ocean. In this scenario, gravity isn't just stuck on our sheet; on very large scales, it starts to "leak" into that extra dimension. This leakage is supposed to act like a natural engine, making the universe speed up without needing any weird dark energy. It's a clever, geometric solution to the mystery.

But does this 5D leaky-sheet idea actually work when we test it against the sharpest data we have? A team of researchers recently put the DGP model through the ultimate stress test using the latest data from the Dark Energy Spectroscopic Instrument (DESI), combined with other cosmic clues like ancient star explosions and the afterglow of the Big Bang.

The Verdict: The Leak Doesn't Work

The results are a bit of a bummer for the DGP fans. The study found that while the DGP model is mathematically interesting, it simply doesn't fit the data we actually see.

When the researchers crunched the numbers, the DGP model predicted that the universe is expanding at a speed of about 63.28 to 64.05 km s⁻¹ Mpc⁻¹. To put that in perspective, the standard $\Lambda$ CDM model (which fits the data much better) predicts a speed closer to 67.4 km s⁻¹ Mpc⁻¹. The DGP model doesn't just miss the mark; it actually pushes the predicted speed further away from the measurements we get from local galaxies. Instead of solving the "Hubble Tension," the DGP model makes the disagreement between different measurements even worse.

Why the Model Fails

The authors found that the DGP model struggles to play nice with two specific types of cosmic evidence at the same time:

The "Baby Picture" (CMB): Data from the Cosmic Microwave Background tells us what the universe looked like when it was a baby.
The "Teenager" (DESI BAO): The new DESI data measures how the universe is stretching right now.

The DGP model tries to stretch the rules to fit the "teenager" data, but in doing so, it breaks the "baby picture." It's like trying to wear a pair of shoes that fit your feet perfectly but are so tight they crush your ankles. The model can't simultaneously satisfy the constraints from the early universe and the recent universe.

The study also looked at whether the universe might be curved (like a saddle or a sphere) rather than flat. Even when they allowed for this extra wiggle room, the DGP model still failed. The data suggests a tiny, slight curve (with a value of 0.0088 ± 0.0016), but this small adjustment wasn't enough to save the theory. The statistical "penalty" for using the DGP model was huge—so huge that the standard model is overwhelmingly preferred.

A Specific Test: The Sound Horizon

One tricky part of the analysis involved the "sound horizon," which is like a cosmic ruler used to measure distances. The researchers tested three ways to use this ruler:

Fixed Ruler: Using a standard length.
Free Ruler: Letting the length change to fit the data.
Self-Consistent Ruler: Calculating the length based on the physics of the DGP model itself.

When they let the ruler be "free," the DGP model suddenly looked like it matched local measurements of the universe's speed (73.57 ± 1.10 km s⁻¹ Mpc⁻¹). However, the authors warn that this is a trick. To get this result, the model had to invent a wildly curved universe that doesn't make physical sense. Once they forced the model to be physically consistent (using the "self-consistent" ruler), the speed dropped back down to 64.05 ± 0.27 km s⁻¹ Mpc⁻¹, and the tension returned. This proves that the apparent success of the "free ruler" was just a mathematical loophole, not a real solution.

The Bottom Line

The paper concludes that the DGP framework, while a fascinating idea about gravity leaking into a fifth dimension, is currently ruled out by high-precision data. It fails to explain the universe's expansion history without creating new problems. The transition from a slowing universe to an accelerating one happened much later in the DGP model (at a redshift of 0.41) compared to the standard model (around 0.67), suggesting the "leaky gravity" engine is too weak to drive the cosmic acceleration we observe.

In short: The universe is expanding, and while gravity leaking into a 5D ocean is a cool concept, the latest measurements from DESI and other telescopes say, "Sorry, that's not how our balloon is inflating." The standard model remains the champion, and the DGP model is left on the bench.

Technical Summary: Cosmological Constraints on the DGP Model in light of DESI DR2 2025 Data

Problem Statement
The late-time acceleration of the Universe remains a central puzzle in cosmology. While the standard $\Lambda$ CDM model attributes this to a cosmological constant, it faces significant theoretical challenges, including the cosmological constant problem and the persistent $\sim 5\sigma$ Hubble tension between early-Universe constraints (Planck) and local distance ladder measurements. Modified gravity theories, such as the Dvali–Gabadadze–Porrati (DGP) braneworld model, offer an alternative geometric explanation where gravity "leaks" into an extra dimension at large scales, driving acceleration without a cosmological constant. However, previous constraints on the DGP framework were limited by the statistical uncertainties and redshift coverage of earlier observational catalogs. This study addresses whether the DGP model can provide a consistent description of cosmic evolution when confronted with the unprecedented precision of the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2).

Methodology
The authors perform a systematic joint likelihood analysis of both flat and non-flat DGP models using a unified dataset comprising:

DESI DR2 BAO: Baryon Acoustic Oscillation measurements from over 14 million galaxies and quasars ( $z \approx 4.2$ ).
Cosmic Chronometers (CC): Direct measurements of the Hubble expansion rate $H(z)$ from 32 passively evolving galaxies.
Type Ia Supernovae (SNIa): The Pantheon sample (1048 SNIa) used as standard candles.
CMB Distance Priors: Compressed likelihoods from Planck 2018 (shift parameter $R$ , acoustic scale $l_A$ , and baryon density $\omega_b$ ).

A critical methodological feature is the self-consistent treatment of the sound horizon. Rather than fixing the sound horizon at the drag epoch ( $r_d$ ) to a fiducial value, the authors compute it dynamically within the DGP framework to ensure consistency between the CMB and BAO sectors. The analysis employs Monte Carlo Markov Chain (MCMC) methods with uniform priors on parameters ( $\Omega_m, \Omega_{rc}, H_0, \Omega_k, \Omega_b h^2$ ). Model performance is evaluated using the minimum $\chi^2$ statistic and the Akaike Information Criterion (AIC) to compare DGP against the standard $\Lambda$ CDM baseline.

Key Contributions

Updated Constraints: The paper provides the most stringent constraints to date on DGP parameters using the latest DESI DR2 data, significantly reducing error margins compared to previous studies (e.g., improving precision on $\Omega_{rc}$ by a factor of ~5 compared to Ref. [45]).
Sound Horizon Calibration Analysis: The study explicitly investigates the impact of sound horizon treatment ( $r_d$ fixed vs. free vs. self-consistent $r_d=r_s$ ). It demonstrates that treating $r_d$ as a free parameter artificially inflates $H_0$ and curvature to match local measurements but violates physical consistency with early-Universe physics.
Dynamical Evolution: The authors reconstruct the deceleration parameter $q(z)$ and the transition redshift $z_t$ , offering a dynamical comparison between DGP and $\Lambda$ CDM expansion histories.

Results

Parameter Constraints:
- Non-flat DGP: $H_0 = 64.05 \pm 0.27$ km s $^{-1}$ Mpc $^{-1}$ , $\Omega_m = 0.3264 \pm 0.0043$ , $\Omega_k = 0.0088 \pm 0.0016$ (indicating a $\sim 5.5\sigma$ preference for an open universe), and a transition redshift $z_t \simeq 0.41$ .
- Flat DGP: $H_0 = 63.28 \pm 0.25$ km s $^{-1}$ Mpc $^{-1}$ and $\Omega_m = 0.3303 \pm 0.0036$ .
Hubble Tension: In both scenarios, the inferred $H_0$ is significantly lower than the Planck $\Lambda$ CDM value ( $67.4 \pm 0.54$ ). Consequently, the DGP framework fails to alleviate the Hubble tension; instead, it exacerbates the discrepancy with local distance ladder measurements.
Model Comparison: The DGP models are strongly disfavored by current data. The $\Delta$ AIC values are $+101.821$ (non-flat) and $+155.253$ (flat) relative to their respective $\Lambda$ CDM baselines. This large statistical penalty is driven primarily by the DGP model's inability to simultaneously accommodate DESI BAO and CMB distance priors.
Dynamics: The DGP model predicts a delayed onset of cosmic acceleration ( $z_t \approx 0.41$ ) compared to $\Lambda$ CDM ( $z_t \approx 0.67$ ), implying a weaker late-time acceleration and systematically higher deceleration parameters $q(z)$ at low redshifts.

Significance and Claims
The paper concludes that the standard DGP framework is unable to simultaneously satisfy early- and late-Universe observational constraints in the era of precision cosmology. While the model offers a geometric alternative to dark energy, the high-precision DESI DR2 data, when combined with CMB priors in a self-consistent manner, rules out the DGP scenario as a viable solution to the current cosmological tensions. The authors assert that the model introduces additional inconsistencies rather than resolving existing ones. The work serves as a consolidated assessment, demonstrating that the modified expansion history inherent to the DGP braneworld scenario is insufficient to explain current cosmological observations without significant theoretical refinement or extensions.

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