Version 1. 1 — 20 March 2026 (extends v1. 0 from 17 March 2026) New in this version: numerical background integration via Runge–Kutta (DOP853), decomposition of the observable sector into standard matter and a coupling-driven dark-energy component, first χ² fit to 29 cosmic chronometer H (z) measurements (χ²/dof = 0. 59), χ² contour map over (λₑff, H₀), parameter degeneracy discussion, and a portable Python script reproducing all figures. --- I present a phenomenological two-sector Friedmann–Robertson–Walker model in which an interaction term Q = λHₓ ρᵧ transfers energy from a hidden sector y into an effective dark-energy component in the observable sector x. At the homogeneous background level, this generates an effective equation of state wₑff = −1 − λρ̃ᵧ/ (3ρ̃de), so that wₑff < −1 whenever the coupling is active. This statement is purely a property of the background equations and should not be interpreted as a result on perturbative stability. Separately, when the model is supplemented by a loop-quantum-cosmology bounce prescription, it admits non-singular cyclic solutions. A first comparison with 29 cosmic chronometer H (z) measurements indicates that the model is not obviously inconsistent with this dataset at background level, with effective coupling λₑff ≡ λr₀ ≈ 0. 52, H₀ ≈ 70. 8 km/s/Mpc, wᵧ = −1. 00, and χ²/dof = 0. 59. Because the reduced χ² lies well below unity and only diagonal chronometer errors are used, this result should be interpreted as a first consistency check rather than as a statistically robust parameter determination. The fitted H₀ lies in an intermediate range relative to commonly quoted CMB- and distance-ladder determinations, but no statement about the Hubble tension is made. No perturbation analysis, BAO, CMB, or supernova comparison is included. This remains an exploratory phenomenological proof of concept.
Finn Lennard Jacobsen (2026) studied this question.