⚛️ general relativity

Entropic Chaplygin-Gas cosmology and late-universe tension diagnostics

This paper demonstrates that an entropic generalized Chaplygin-gas cosmology can effectively alleviate the $H_0$ tension by modifying late-time background expansion while leaving the $S_8$ discrepancy largely unaffected, suggesting these cosmological tensions originate from distinct physical sectors.

Original authors: Kelvis A. Kulhkampa, Carlos H. Coimbra-Araújob, Abraão J. S. Capistrano, Luiz A. Cabral, José A. P. F. Marão

Published 2026-07-28

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CC BY 4.0

Original authors: Kelvis A. Kulhkampa, Carlos H. Coimbra-Araújob, Abraão J. S. Capistrano, Luiz A. Cabral, José A. P. F. Marão

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 stuff is inside it pushing the walls outward. This invisible stuff is called "dark energy," and the stuff holding the balloon together is "dark matter." Together, they make up the "dark sector," which is the mysterious majority of our cosmos, even though we can't see it directly.

The problem is that when scientists measure the universe's expansion using different tools, they get different answers. It's like asking two groups of people to measure the same room: one group uses a laser tape measure and gets 12 feet, while the other uses a ruler and gets 14 feet. This disagreement is called "cosmological tension." The most famous disagreement is about the Hubble constant ( $H_0$ ), which tells us the current speed of the universe's expansion. Another big disagreement involves $S_8$ , which measures how clumpy the universe is. If our standard model of the universe (called $\Lambda$ CDM) is correct, these measurements should match perfectly. Since they don't, scientists are on the hunt for a new theory that can fix the math and make the measurements agree.

In this paper, a team of researchers investigates a new idea called "Entropic Chaplygin-Gas cosmology" to see if it can reshape the parameters underlying these cosmic arguments. Think of the standard model as having two separate ingredients in the cosmic soup: one for dark matter (which clumps together to form galaxies) and one for dark energy (which pushes everything apart). The Chaplygin gas idea suggests that these two ingredients are actually just one single, magical fluid that changes its personality over time. In the early universe, this fluid acted like heavy, clumpy matter, but as the universe got older, it slowly transformed into a smooth, pushing force like dark energy.

However, there's a catch. In its simplest form, this single fluid acts a bit weirdly when it tries to clump together; it creates ripples and oscillations that don't match what we see in the real universe. To fix this, the authors use a "thermodynamic" trick involving entropy (a measure of disorder) to make the fluid behave more like normal matter when it comes to clumping, while still acting like dark energy when it comes to expansion. They call this the "Entropic" version.

The researchers tested this new model against a massive pile of real-world data. They looked at the light from exploding stars (supernovae), the echoes of sound waves from the early universe (BAO), and the way galaxies are moving (RSD). They compared their new "one-fluid" model against the standard "two-ingredient" model using two different sets of supernova data: one called PantheonPlus+SH0ES (PPS) and another called DES–Dovekie.

Here is what they found, and it depends entirely on which set of data you trust. When they used the PPS data, their new model looked like a strong contender. It partially relaxed discrepancies specifically associated with the background expansion history, shifting the preferred parameters for the universe's growth. However, the paper notes that this shift leaves the discrepancies related to how structures grow (the $S_8$ tension) comparatively robust and unresolved. Furthermore, the authors explicitly warn that the strong preference for this model using PPS data might be an artifact of that specific dataset's calibration, requiring careful auditing before it can be trusted as a real solution. When they switched to the DES–Dovekie data, the story changed completely. In this case, the new model didn't offer any real improvement over the standard model; in fact, the standard model looked slightly better because it was simpler.

The authors conclude that their "Entropic Chaplygin Gas" model is a fascinating theoretical playground that requires a more qualified interpretation and is not a definitive solution to the cosmic tensions yet. The results are highly sensitive to which specific measurements of exploding stars are used. If the PPS data is right, the new model might help resolve some of the background-driven discrepancies, but the paper cautions that this preference is likely a dataset artifact. If the DES–Dovekie data is right, the standard model is still the champion. The paper suggests that the tension between early and late universe measurements might not be solved by a single magic fluid, but rather that different parts of the universe might need different explanations. Until we get more precise data, the mystery of the dark sector remains unsolved, but this new "entropic" idea gives scientists a fresh, flexible tool to keep testing.

Technical Summary: Entropic Chaplygin-Gas Cosmology and Late-Universe Tension Diagnostics

Problem Statement
Persistent discrepancies between early-Universe (e.g., Cosmic Microwave Background) and late-Universe (e.g., Type Ia supernovae) measurements have established cosmological tensions, particularly regarding the Hubble constant ( $H_0$ ) and the matter fluctuation amplitude ( $S_8$ ), as critical stress tests for the standard $\Lambda$ CDM paradigm. While the $\Lambda$ CDM model successfully explains accelerated expansion, it lacks a fundamental theoretical explanation for the cosmological constant ( $\Lambda$ ) and the nature of Cold Dark Matter (CDM). Unified Dark Matter-Dark Energy (UDM) models, such as the Chaplygin gas, offer a phenomenological alternative by interpolating between dust-like matter at early times and a dark energy-dominated regime at late times. However, standard adiabatic Chaplygin gas models face severe theoretical difficulties at the perturbative level, specifically generating large effective sound speeds that induce oscillations in the matter power spectrum and suppress structure formation, leading to conflicts with observational data.

Methodology
This work investigates an entropic generalized Chaplygin gas (gCg) model, where the pressure depends not only on density but also on entropy. This entropic extension allows for a thermodynamically consistent description that can decouple the background evolution from the perturbative clustering properties.

The study employs a combined background and growth analysis using the following datasets:

Supernovae: Two distinct compilations are tested: PantheonPlus+SH0ES (PPS) and the DES–Dovekie recalibration.
Large Scale Structure: DESI Baryon Acoustic Oscillation (BAO) measurements and Redshift-Space Distortion (RSD) growth data ( $f\sigma_8$ ).
CMB: Compressed Planck 2018 distance priors and a Planck lensing-amplitude prior.

Perturbative Treatment:
To address the sound speed instability of standard gCg models, the authors adopt a non-adiabatic prescription. They define an effective rest-frame sound speed ( $c^2_{\text{eff}}$ ) and impose the condition $c^2_{\text{eff}} \simeq 0$ . This effectively cancels the adiabatic pressure-gradient contribution responsible for acoustic oscillations, allowing the unified dark fluid to cluster similarly to CDM while maintaining the desired background expansion history.

Numerical Implementation:
Parameter estimation is performed using the MultiNest nested-sampling algorithm to handle the non-Gaussian, highly degenerate, and potentially multimodal nature of the gCg parameter space. The analysis compares the entropic gCg model against the standard flat $\Lambda$ CDM model. Model selection is evaluated using the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and Deviance Information Criterion (DIC). Tension diagnostics are conducted using the Tensiometer code to quantify posterior shifts in the common derived parameter space $(H_0, \Omega_m, S_8)$ .

Key Results

Background Evolution: The entropic gCg model reproduces a background expansion history ( $H(z)$ , $q(z)$ , $w(z)$ ) that is close to $\Lambda$ CDM, successfully interpolating between matter-like behavior at high redshift and dark energy-like behavior at late times. The transition redshift ( $z_t$ ) is found to be consistent with observational constraints ( $z_t \approx 0.64$ ).
Dataset Dependence: The statistical performance of the model is highly sensitive to the supernova compilation used:
- PantheonPlus+SH0ES (PPS): The gCg model shows a substantial improvement in fit ( $\Delta\chi^2_{\text{min}} \approx -301.7$ ) compared to $\Lambda$ CDM. It produces a large displacement in the $(H_0, \Omega_m, S_8)$ parameter space and is strongly preferred by all information criteria (Bayes factor $\sim 10^{63}$ ).
- DES–Dovekie: The gCg model yields a negligible improvement in fit ( $\Delta\chi^2_{\text{min}} \approx -0.45$ ). The posterior contours for gCg and $\Lambda$ CDM largely overlap in the derived parameter space. Information criteria (AIC, BIC, DIC) and Bayesian evidence mildly to moderately favor the standard $\Lambda$ CDM model.
Tension Diagnostics: Using Tensiometer, the study finds that the joint constraints for gCg and $\Lambda$ $Λ$ CDM are displaced mainly along background-sensitive directions.
- For the PPS configuration, the posterior shift is saturated ( $P_{\text{shift}} \approx 1$ ), indicating a displacement beyond the stable range of the estimator.
- For the DES–Dovekie configuration, the shift is minimal ( $0.355 \pm 0.005 \sigma$ ).
- The model preferentially modifies the late-time expansion sector, reducing background-related discrepancies (particularly those associated with $H_0$ ) while leaving residual growth discrepancies ( $S_8$ ) comparatively robust.

Significance and Claims
The paper concludes that the entropic generalized Chaplygin gas serves as a useful theoretical laboratory for unified dark sector cosmology. It demonstrates that a unified fluid can mimic both CDM and DE across different epochs. However, the authors explicitly state that the model's ability to alleviate cosmological tensions is not dataset-independent. The strong preference for gCg observed with the PPS compilation is not reproduced with the DES–Dovekie compilation, suggesting that the late-time supernova calibration is the dominant factor controlling model comparison outcomes.

The authors emphasize that while the entropic prescription ( $c^2_{\text{eff}} \simeq 0$ ) improves phenomenological viability by allowing CDM-like clustering, the current analysis relies on compressed background observables and effective growth approximations rather than a full Einstein–Boltzmann evolution. Consequently, the results should be interpreted as joint background and compressed-growth constraints. The paper posits that a robust assessment of the model requires future implementation in a full Einstein–Boltzmann solver to consistently treat non-adiabatic perturbations and the full CMB likelihood, particularly to address the complexities of the $w \to -1$ regime.

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