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Extended Entropic Dark Energy with Four Free Parameters: Theory, Dynamics, and Constraints

Davood Momeni

TL;DR

The paper develops a curved FLRW cosmology driven by a four-parameter entropic dark energy model, linking generalized horizon entropy to modified Friedmann dynamics. It derives closed-form expressions for the Hubble rate $H(z)$, dark-energy density fraction $\Omega_D(z)$, and the effective equation of state $w_D(z)$, enabling analytic exploration of the expansion history across parameter space. The study identifies viable regions, notably with $\beta>1$ and small positive curvature $\Omega_k$, that can raise the local $H_0$ value toward SH0ES measurements while remaining consistent with CC, BAO, and Pantheon+ data. Dynamical-system analysis reveals a late-time de Sitter attractor and a matter-dominated saddle, illustrating a realistic transition from deceleration to acceleration without extra fields, and the work outlines concrete paths for incorporating perturbations, Bayesian inference, and connections to quantum-gravitational entropy concepts in future research.

Abstract

We investigate a four-parameter entropic dark energy model in a spatially curved FLRW universe, based on a generalized entropy-area relation at the apparent horizon. While the proposed entropy function captures a broad class of gravitational entropy corrections, including Bekenstein-Hawking, Tsallis, and power-law forms, it does not encompass information-theoretic entropies such as Sharma-Mittal or Renyi. Within this framework, we derive exact analytical expressions for key cosmological observables, including the Hubble parameter $H(z)$, the dark energy density parameter $Ω_D(z)$, and the equation of state $w_D(z)$. A comprehensive parameter-space analysis reveals viable regions, particularly for $β> 1$ and small positive curvature, that accommodate elevated $H_0$ values consistent with recent SH0ES measurements. Our results offer a simple and analytically tractable alternative to conventional dynamical dark energy models, with potential relevance to the ongoing Hubble tension.

Extended Entropic Dark Energy with Four Free Parameters: Theory, Dynamics, and Constraints

TL;DR

The paper develops a curved FLRW cosmology driven by a four-parameter entropic dark energy model, linking generalized horizon entropy to modified Friedmann dynamics. It derives closed-form expressions for the Hubble rate , dark-energy density fraction , and the effective equation of state , enabling analytic exploration of the expansion history across parameter space. The study identifies viable regions, notably with and small positive curvature , that can raise the local value toward SH0ES measurements while remaining consistent with CC, BAO, and Pantheon+ data. Dynamical-system analysis reveals a late-time de Sitter attractor and a matter-dominated saddle, illustrating a realistic transition from deceleration to acceleration without extra fields, and the work outlines concrete paths for incorporating perturbations, Bayesian inference, and connections to quantum-gravitational entropy concepts in future research.

Abstract

We investigate a four-parameter entropic dark energy model in a spatially curved FLRW universe, based on a generalized entropy-area relation at the apparent horizon. While the proposed entropy function captures a broad class of gravitational entropy corrections, including Bekenstein-Hawking, Tsallis, and power-law forms, it does not encompass information-theoretic entropies such as Sharma-Mittal or Renyi. Within this framework, we derive exact analytical expressions for key cosmological observables, including the Hubble parameter , the dark energy density parameter , and the equation of state . A comprehensive parameter-space analysis reveals viable regions, particularly for and small positive curvature, that accommodate elevated values consistent with recent SH0ES measurements. Our results offer a simple and analytically tractable alternative to conventional dynamical dark energy models, with potential relevance to the ongoing Hubble tension.

Paper Structure

This paper contains 12 sections, 29 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Generalized Entropy and Friedmann Equations
  4. Closed-form Expressions
  5. Hubble Expansion Rate
  6. Dark Energy Density Fraction
  7. Equation of State, Deceleration, and Analytic Features
  8. Analytical Parameter Space Setup
  9. Comparison with Observational Data
  10. Dynamical system analysis
  11. Discussion and Viable Regions
  12. Conclusion and Outlook

Figures (1)

  • Figure 1: Phase-space portrait in the $(x, y)$ plane showing critical points A (saddle) and B (stable attractor). Arrows represent flow directions for $w_g = -1$.