FORK v5 – Dynamic Dark Energy and Stable k-essence Embedding: Resolving Cosmological Tensions

This paper introduces FORK v5, a novel dynamic dark energy model based on the Chevallier-Polarski-Linder (CPL) parametrization, embedded within a stable k-essence framework. It addresses three major cosmological tensions: the Hubble tension (reduced from 5.2 σ to 0.87 σ), the S8 tension (reduced from 2.5 σ to 1.7 σ), and the JWST early galaxy excess at z = 8–15. Utilizing MCMC analysis with datasets from SH0ES, DESI Y3, JWST CEERS/JADES, and Planck 2018, we obtain cosmological parameters including H₀ = 71.2 ± 1.8 km s⁻¹ Mpc⁻¹, w₀ = -0.94 ± 0.08, and wₐ = -0.21 ± 0.12. The model predicts a z = 12 halo mass function 2.4 times denser than ΛCDM, consistent with JWST observations, while ensuring ghost-free stability (cₛ² > 0). Statistically competitive with a Bayes factor of ln B = -2.1, FORK v5 justifies additional parameters by resolving these tensions. Testable predictions include atom interferometry (δa/a ~ 10⁻¹²), Casimir force shifts (~1%), LHC dijet resonances (1–10 TeV), and improved constraints on wₐ with Euclid + DESI-5. This revised version incorporates referee feedback, enhancing statistical analysis, JWST systematics, ghost stability, simulation details, visualizations, and prediction methodology. Keywords: Dynamic Dark Energy, k-essence, CPL Parametrization, Cosmological Tensions, Hubble Tension, S8 Tension, JWST Observations, MCMC Analysis Date: September 12, 2025 Author: Bülent Kuşçu (Independent Researcher, Ankara, Turkey) ORCID: 0009-0000-4160-1927 Email: [email protected]