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

TL;DR

This paper introduces a four-parameter entropic dark energy model in curved universe, deriving analytical expressions for cosmological parameters, and identifies viable parameter regions that align with recent Hubble constant measurements, potentially addressing the Hubble tension.

Contribution

It presents a novel four-parameter entropic dark energy model with analytical solutions, broad entropy considerations, and constraints consistent with current cosmological observations.

Findings

Viable parameter regions for $eta > 1$ and small positive curvature.

Analytical expressions for $H(z)$, $ ho_D(z)$, and $w_D(z)$.

Model accommodates elevated $H_0$ values consistent with recent measurements.

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 $\Omega_D(z)$, and the equation of state $w_D(z)$. A comprehensive parameter-space analysis reveals viable regions, particularly for $\beta > 1$ 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.