From linear w-γ correlation to redshift-dependent dynamics: A complete phenomenological framework and testing roadmap for dark energy

Tongfeng  Zhao

doi:10.59400/adecp4007

From linear w-γ correlation to redshift-dependent dynamics: A complete phenomenological framework and testing roadmap for dark energy

Tongfeng Zhao
Independent Researcher, Guangzhou 510000, China

Article ID: 4007

Keywords: dark energy; phenomenological model; structure growth index; Hubble tension; hierarchical Bayesian model comparison; effective gravitational constant; redshift; interacting dark sectors

Abstract

Based on an adaptive universe model, this perspective article presents a phenomenological framework that correlates the dark energy equation of state w with the cosmic growth index γ via the linear relation w(a) = −1 + η(γ(a) − 0.55). Recognizing that the coupling between dark energy and structure formation may evolve with cosmic time, the framework is extended to a redshift-dependent formulation: w(z) = −1 + η(z)[γ(z) − 0.55] + Δw_bg(z), where η(z) captures the structure-dependent coupling and Δw_bg(z) accounts for intrinsic background evolution. Several physically motivated parameterizations of η(z) are proposed, including continuous forms (smooth transition and oscillatory) and a phenomenological piecewise model aligned with distinct phases of structure formation history. Built upon an interacting dark sector model that strictly conserves energy and momentum, the framework maintains the spacetime geometry of General Relativity while naturally addressing both the Hubble tension (via enhanced late-time expansion) and the S₈tension (via suppressed structure growth). A hierarchical Bayesian testing roadmap with Fisher forecasts demonstrates that upcoming surveys (DESI, Euclid, Roman) can decisively detect couplings of magnitude |η| ≳ 0.05 at high significance. The framework yields distinctive, testable predictions—including correlated w(z) and fσ₈(z) evolution, a gravitational slip parameter η_slip= 1 that distinguishes it from modified gravity theories, and scale-dependent signatures in the nonlinear regime—providing a comprehensive path to either validate or falsify the hypothesized dark energy–structure growth connection.

Published

2026-04-16

How to Cite

Zhao, T. (2026). From linear w-γ correlation to redshift-dependent dynamics: A complete phenomenological framework and testing roadmap for dark energy . Advances in Differential Equations and Control Processes, 33(2). https://doi.org/10.59400/adecp4007

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Issue

Vol. 33 No. 2 (2026) in progress:

Section

Perspective

This work is licensed under a Creative Commons Attribution 4.0 International License.

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