⚛️ high-energy theory

Conformal Killing Gravity: New Constraints from DESI DR2 BAO datasets

This paper investigates Conformal Killing Gravity, a geometric framework where dark energy emerges from conformal Killing symmetry without empirical parametrization, and finds that constraints from recent cosmological datasets (including DESI DR2 and Planck PR4) favor a quintessence-like evolution approaching a cosmological constant while predicting a future expansion turning point, though the model fails to fully resolve the $H_0$ tension.

Original authors: Himanshu Chaudhary, Salvatore Capozziello, Carlo Alberto Mantica, Luca Guido Molinari, Dhruba Jyoti Gogoi, Ghulam Mustafa

Published 2026-08-11

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CC BY 4.0

Original authors: Himanshu Chaudhary, Salvatore Capozziello, Carlo Alberto Mantica, Luca Guido Molinari, Dhruba Jyoti Gogoi, Ghulam Mustafa

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 that balloon is inflating and what's pushing it to expand faster and faster. This mystery is called "dark energy." It's the invisible force that makes up most of the universe, but we can't see it or touch it; we only know it's there because galaxies are running away from each other. The standard story, known as the "ΛCDM" model, says this force is a constant, unchanging push, like a steady hand on the balloon. But lately, the numbers don't quite add up. When scientists look at the baby universe (the Cosmic Microwave Background) and when they look at the grown-up universe (nearby supernovae and galaxy clusters), they get different answers about how fast things are moving. It's like trying to measure a car's speed by looking at its engine versus looking at its tires, and getting two different numbers. This confusion has scientists scratching their heads, wondering if the standard story is missing a piece of the puzzle.

Enter a new idea called "Conformal Killing Gravity" (CKG). Instead of inventing a mysterious new substance to explain the acceleration, this theory suggests the answer is hidden in the shape of space-time itself. Think of the universe not just as a stage where things happen, but as a flexible fabric that has its own built-in rules for stretching. In this paper, the authors propose that the acceleration we see is a natural result of these geometric rules, specifically a symmetry called "conformal Killing symmetry." It's as if the balloon has a built-in elasticity that changes as it gets bigger, creating a push without needing a mysterious "dark" hand. The authors wanted to test this geometric idea against the most recent and precise data we have to see if it fits better than the standard story.

The team took the CKG model and ran it through a massive digital gauntlet using the latest data from the Dark Energy Spectroscopic Instrument (DESI) and the Planck satellite. They compared the geometric model against the standard "constant push" model using billions of data points from the cosmic microwave background, galaxy clusters, and exploding stars (Type Ia supernovae). What they found is fascinating: the geometric model works surprisingly well. It suggests that the "push" of dark energy isn't a constant, but something that changes over time, behaving more like a "quintessence" (a dynamic energy) than a rigid constant. However, there's a catch. Because this geometric push only kicks in after the universe was already formed (after the "recombination" era), it doesn't change the early history of the universe. This means the model cannot fix the famous "Hubble Tension"—the disagreement about how fast the universe is expanding right now. The sound horizon (the cosmic ruler used to measure speed) stays the same, so the tension remains.

Despite not fixing the speedometer disagreement, the CKG model gets a thumbs-up from the data in other ways. The authors found that the model is statistically preferred over the standard model, meaning the data "likes" this geometric explanation more. It predicts that the universe is currently accelerating, but that this acceleration will eventually slow down and stop at a specific point in the future, around a redshift of -0.8 to -0.7, before the universe hits a theoretical limit. The paper also confirms that the model is fully consistent with current weak-lensing measurements regarding the "clumpiness" of the universe (the S8 tension), showing no significant conflict with these observations. In short, the paper suggests that the universe's expansion might be driven by the geometry of space itself, offering a simpler, more natural explanation for why things are speeding up, even if it doesn't solve every mystery in the cosmic book.

Technical Summary: Conformal Killing Gravity and Constraints from DESI DR2 BAO Datasets

Problem Statement
The standard $\Lambda$ CDM cosmological model, while robust against many observations, faces persistent theoretical challenges regarding the fine-tuning and cosmic coincidence problems associated with the cosmological constant. Furthermore, observational anomalies, specifically the $H_0$ and $S_8$ tensions, indicate significant discrepancies between early-Universe inferences (CMB) and late-time local probes. Recent data from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) Baryon Acoustic Oscillation (BAO) measurements have shown a preference for a dynamical dark energy equation of state over a static cosmological constant. This motivates the investigation of geometric alternatives to General Relativity that can naturally generate a dark energy component without invoking exotic matter or empirical parametrizations.

Methodology
The authors investigate Conformal Killing Gravity (CKG), a geometric framework where the dark energy sector emerges from the conformal Killing symmetry of the Robertson–Walker (RW) space-time. In this theory, a divergence-free conformal Killing tensor acts as an effective perfect fluid, introducing a single additional density parameter, $\Omega_D$ , which governs the post-recombination expansion history.

To constrain the CKG model, the authors performed a high-precision Markov Chain Monte Carlo (MCMC) analysis using the Cobaya package. The analysis utilized a comprehensive combination of cosmological datasets:

CMB: Planck PR4 (NPIPE) temperature, polarization, and lensing likelihoods (CamSpec), combined with ACT DR6 CMB lensing data.
BAO: DESI DR2 measurements covering the redshift range $0.3 \leq z \leq 2.33$ .
Supernovae: Three independent Type Ia supernova compilations: Pantheon+, DES-Dovekie, and Union3.

The study compared the CKG model against the standard $\Lambda$ CDM paradigm using Bayesian model comparison (calculating the Bayes factor) and evaluated the model's ability to alleviate the $H_0$ and $S_8$ tensions. Theoretical predictions were computed using the CAMB code.

Key Contributions and Results

Geometric Origin of Dark Energy: The study demonstrates that the CKG framework naturally yields a dynamical dark energy component where the density, pressure, and equation of state ( $w_D$ ) are uniquely determined by the underlying geometry. The model recovers the $\Lambda$ CDM limit when the geometric contribution vanishes ( $\Omega_D = 0$ ).
Equation of State Evolution: The analysis reveals that the CKG model favors a quintessence-like evolution ( $w_D > -1$ ) with no evidence for phantom crossing ( $w_D < -1$ ). The reconstructed equation of state rapidly approaches the cosmological constant value ( $w = -1$ ) at earlier cosmic times ( $z \gtrsim 1$ ), suggesting that dynamical effects are confined to the late Universe.
Future Critical Redshift: A distinct prediction of the model is the existence of a future critical redshift $z_c$ where the Hubble expansion rate vanishes ( $H(z_c)=0$ ). The analysis constrains this value to the range $-0.8 \lesssim z_c \lesssim -0.7$ , indicating that the current accelerated expansion will eventually reach a turning point before the formal singular limit at $z = -1$ .
$H_0$ Tension: The authors find that the CKG model cannot provide a complete solution to the $H_0$ tension. Because the geometric contribution scales as $(1+z)^{-2}$ , it is strongly suppressed during the pre-recombination epoch. Consequently, the sound horizon ( $r_d$ ) remains essentially unchanged compared to $\Lambda$ CDM. While the model yields a slightly higher $H_0$ than standard CMB-only analyses, the tension with local Riess measurements remains significant (approx. 2.65 $\sigma$ to 4.33 $\sigma$ depending on the dataset combination).
$S_8$ Tension: The model remains fully consistent with current weak-lensing constraints on $S_8$ . The inferred values show tensions of less than 0.1 $\sigma$ with KiDS-Legacy and less than 1.8 $\sigma$ with DES Y6, indicating no significant $S_8$ tension.
Statistical Viability: Bayesian evidence analysis yields strong evidence in favor of the CKG model over the standard $\Lambda$ CDM model across all dataset combinations (with $\ln B$ values ranging from -5.53 to -6.84). The model provides a better best-fit description of the data, particularly when Type Ia supernova observations are included.

Significance and Claims
The paper claims that Conformal Killing Gravity provides a simple, physically motivated, and observationally favored framework for describing the late-time accelerated expansion of the Universe. Unlike phenomenological models that assume a specific dark energy parametrization, CKG derives the dark energy behavior directly from the conformal Killing symmetry of space-time.

The authors assert that while the model does not resolve the $H_0$ tension due to its geometric nature affecting only the post-recombination history, it successfully addresses the $S_8$ consistency and is statistically preferred over $\Lambda$ CDM. The results suggest that the origin of dark energy could be fundamentally geometric, offering a viable alternative to the standard cosmological constant that is consistent with the latest DESI DR2, Planck PR4, and supernova data. Future high-precision surveys (e.g., Euclid, LSST, Roman, DESI DR3, CMB-S4) are identified as necessary to further test the subtle deviations from $\Lambda$ CDM predicted by this framework.

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