Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence

arXiv:2603.23551 · gr-qc, astro-ph.CO, hep-th · Submitted 2026-03-22 · Read on arXiv

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Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Next we'll be talking about the paper "Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence".

Jocelyn: The paper was written by Chen-Hao Wu and Yen Chin Ong from Center for the Cross-disciplinary Research of Space Science and Quantum-technologies and College of Physics, Nanjing University of Aeronautics and Astronautics.

Vera: Stay tuned as we take you through the paper and discuss its implications.

Title: Vera: We're shifting gears now to the paper "Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence" by Chen-Hao Wu and Yen Chin Ong.

Jocelyn: That's a massive title, Vera, but it seems to point toward a very specific idea about how the universe works at its most fundamental level.

Vera: It does, and it focuses on how the entropy at a horizon might actually change the strength of gravity.

Subrahmanyan: To put that in perspective, they are using what they call the GEVAG framework to show that any change to the standard area law for entropy forces the gravitational constant to become area-dependent.

Jocelyn: So instead of G being a fixed number, it's actually something that evolves as the universe expands or contracts?

Subrahmanyan: Precisely, because as the horizon area changes, the effective gravitational coupling, or G eff, adjusts itself to keep the thermodynamics consistent.

Vera: It's a complete departure from the way we usually teach General Relativity in textbooks.

Jocelyn: I wonder if this means our current measurements of gravity are just a snapshot of a much more dynamic process.

Subrahmanyan: That is a very insightful way to put it, Jocelyn, as the model suggests the value of G we measure today is just the low-energy limit where these corrections become tiny.

Vera: It really makes you wonder what was happening when those corrections were much larger in the early universe.

Summary: Vera: Now that we've covered the basic concept, let's look at the two very different paths the authors found depending on the sign of that logarithmic correction.

Jocelyn: It's fascinating that a single parameter, the coefficient, can lead to such wildly different cosmic histories.

Subrahmanyan: It really does, because if that coefficient is negative, which is what Loop Quantum Gravity suggests, the universe hits a maximum density.

Vera: You mean it doesn't actually start from a point of infinite density?

Subrahmanyan: Exactly, the density just saturates at a critical value, which effectively prevents the Big Bang singularity from ever occurring.

Jocelyn: That sounds like a much more stable way to start the universe than the classical model.

Subrahmanyan: It is, and it provides a thermodynamic reason for the discreteness of space that many theorists have been looking for.

Vera: But what happens if that coefficient is positive, like in the Asymptotic Safety scenario?

Subrahmanyan: In that case, gravity actually gets weaker in the high-energy limit, with G eff approaching zero as the energy scale goes up.

Jocelyn: That sounds like it could solve some of the problems we have with the very beginning of time.

Subrahmanyan: It actually does, because it leads to a scaling where the Hubble parameter relates to density in a much gentler way.

Vera: And that leads us directly into how this might change our understanding of inflation.

Improvements: Vera: We've seen the two different outcomes, but I want to focus on why the GEVAG approach is considered a major improvement over older methods.

Jocelyn: You're talking about how they avoid those mathematical glitches that popped up in previous entropic models, right?

Vera: Yes, specifically those "sudden singularities" that would cause the acceleration of the universe to blow up mathematically.

Subrahmanyan: That's a crucial point, because in older models where G was kept fixed, the math would break down even when the energy density was finite.

Jocelyn: So by letting G vary alongside the entropy, they've basically smoothed out the entire evolutionary path?

Subrahmanyan: They have, because they ensure the Bianchi identity remains satisfied by modifying the conservation law for matter.

Vera: I noticed they mentioned that the energy-momentum tensor isn't independently conserved anymore.

Subrahmanyan: That's right, there's an actual exchange of energy between the matter sector and the geometry itself.

Jocelyn: It's a much more integrated way of looking at the cosmos, where matter and space are constantly trading energy.

Vera: It makes the whole system feel much more self-consistent than the older, more "patched-on" versions of these theories.

Jocelyn: It's also interesting how this leads to a more natural onset for inflation in the positive branch.

Conclusion: Vera: It has been a deep dive into the mechanics of spacetime, and we're coming to the end of our look at "Cosmology with Logarithmic Corrected Horizon Entropy According to the Generalized Entropy and Variable-G Correspondence."

Jocelyn: This paper really challenges the idea that the fundamental constants of nature are just static numbers.

Subrahmanyan: It provides a beautiful link between the microscopic laws of quantum gravity and the macroscopic evolution of the entire universe.

Vera: And it gives us a way to test these ideas, even if the effects are tiny in the modern era.

Jocelyn: I'm looking forward to seeing if future surveys can find any hint of this running G.

Subrahmanyan: It certainly moves us closer to a unified picture where thermodynamics and gravity are two sides of the same coin.

Vera: Thanks for joining us for this discussion, and we'll be back next time to look at something completely different.

Jocelyn: See you then!

Chen-Hao Wu, Yen Chin Ong

Center for the Cross-disciplinary Research of Space Science and Quantum-technologies · College of Physics, Nanjing University of Aeronautics and Astronautics

gr-qc, astro-ph.CO, hep-th

Submitted: 2026-03-22

Updated: 2026-08-24

Journal ref: JHEP 08 (2026) 145

DOI: 10.1007/JHEP08(2026)145

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 62/100

The gist: This paper investigates the cosmological implications of incorporating logarithmic quantum-gravitational corrections into the horizon entropy within the "Generalized Entropy Varying-G" (GEVAG)

Key concepts

Variable-G Correspondence
This framework suggests that the gravitational constant, G, is not a fixed number but changes (varies) depending on the entropy of the horizon. This change is necessary to keep the thermodynamics of the universe consistent as it evolves.
Generalized Entropy and Variable-G Approach (GEVAG)
This method uses generalized entropy to show that any deviation from standard area laws for entropy forces G to become dependent on area. It provides a framework where gravitational coupling adjusts itself as the horizon area changes.
Logarithmic Correction Coefficient ($\tilde{c}$)
This single parameter determines the cosmic history predicted by the model. If it is negative, it prevents a Big Bang singularity; if positive, gravity weakens at very high energy scales.
Bianchi Identity
In this context, satisfying the Bianchi identity is crucial because it ensures that when G varies with entropy, the entire evolutionary path remains mathematically consistent and avoids singularities.

Terminology

Summary

This paper investigates the cosmological implications of incorporating logarithmic quantum-gravitational corrections into the horizon entropy within the Generalized Entropy Varying-G (GEVAG) framework. The central premise of the GEVAG framework is that any modification to the Bekenstein-Hawking area law would also lead to a varying-G gravity theory in which the effective gravitational constant G eff becomes area-dependent. The authors specifically examine the logarithmic correction, expressed as S = A over 4G + (A over G), where is a model-dependent dimensionless parameter.

The GEVAG Framework and Mathematical Foundation

The study adopts a thermodynamic perspective based on the principle that the Clausius relation delta Q = T dS holds for all local causal horizons. In the GEVAG framework, this leads to a modified continuity equation grad a (G eff T ab) = 0, representing an energy exchange between the geometry and the matter sector. For a flat FLRW universe, the effective gravitational coupling is derived as G eff(H) = G over 1 + epsilon(H), where the dimensionless correction term is defined as epsilon(H) G H squared over pi.

Cosmological Evolution: Two Distinct Scenarios

The research reveals that the sign of the coefficient dictates two fundamentally different cosmological histories:

  1. The < 0 Case (Density Saturation): This scenario, favored by LQG, results in a fundamental bound on the matter energy density, which prevents the Universe from collapsing into a singularity. The authors find that the classical Big Bang singularity rho crit to infinity is dynamically forbidden because the modified Friedmann constraint imposes a density saturation. The maximum density is determined to be rho crit = 3 over 32G squared, at which point the maximum effective gravitational coupling is G eff(H) = 2G. Furthermore, the GEVAG approach can evade the sudden singularity that could otherwise arise when the coefficient of the logarithmic correction term is negative in constant- G approaches.

  2. The > 0 Case (Asymptotic Safety): This scenario, often discussed in the context of ASG, leads to a regime where the vanishing of G eff in the UV limit realizes the asymptotic safety scenario. In the high-energy limit, the scaling relation becomes H about (8 pi over 3 G) 1/4 rho 1/4, which contrasts sharply with the classical GR scaling H proportional to rho 1/2. This branch ameliorates the 'arrow of time' problem because the effective gravitational constant becomes very small in the early Universe.

Implications for Inflationary Conditions

The paper analyzes how these modifications affect the naturalness of initiating a subsequent period of slow-roll inflation.

  • In the ** > 0 branch**, slow-roll inflation becomes more natural. The modified equation of motion for the inflaton field shows that the friction term doubles (changing from the standard 3H to 6H in the denominator of the velocity relation about-V'over 6H), and the dependence on V 3/2 in the denominator... naturally relaxes the constraint on the slope V.

  • In the ** < 0 branch**, the inflationary condition is similar to the GR case, and the first slow-roll parameter epsilon H maintains the same order of magnitude as in standard General Relativity.

Thermodynamic Consistency and Parameter Constraints

The authors verify the generalized second law (GSL): total = h + m at least 0. They conclude that for the 0 branch, the GSL does not hold automatically during inflation but imposes specific constraints on the dynamics of inflation. Regarding the parameter, the authors suggest that about O(1) is a natural prediction for the asymptotic safety scenario, noting that this value is consistent with black hole entropy counting in LQG.

Improvements for AI systems

(Note: Given the extreme stakes, the following improvements focus on building highly specialized, verifiable computational modules rather than general AI enhancements. These systems are designed to handle the complex mathematical structures inherent in quantum gravity and cosmology.)

Mechanism: The AI system must be upgraded with a specialized PINN architecture trained on the highly non-linear partial differential equations governing modified gravity theories (G mu nu to f(R) or f(T)). This module will replace standard numerical solvers when simulating the evolution of highly curved, time-dependent backgrounds (like those encountered during inflation or near apparent horizons).

What the Improved AI System Can Do:

  • Simulate Cosmic History: It can accurately model the full cosmological evolution from a hypothesized Planck-scale initial condition through reheating and until the current epoch, handling transitions between different gravitational regimes (e.g., solving for the transition from quantum gravity effects to standard General Relativity).

  • Analyze Horizon Dynamics: It can calculate the time-dependent thermodynamics of apparent horizons (R mu nu) under varying conditions (like those proposed by background structures or modified energy components), providing precise predictions for entropy flow and temperature changes that are currently subject to confusions in the literature.

  • Solve Modified Field Equations: It can solve Einstein's equations when the gravitational constant (G) or other fundamental parameters are allowed to vary over time, providing robust solutions for alternatives to the cosmological constant.

Sources

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