We present a cosmological model in which the effective gravitational constantGeff (z) runs with redshift as a consequence of the renormalization group (RG) flowof spin-network degrees of freedom in the framework of Loop Quantum Gravity(LQG) combined with Multi-scale Entanglement RenormalizationAnsatz (MERA) tensor networks. The running takes the form Geff (z) = GN 1 − ε(z) , where ε(z) =ε0 /(1 + (z/zc )n ) is derived analytically from the fixed-point structure of the spin RGflow, not assumed ad hoc. We supplement the model with a dark-energy–dark-mattercoupling term Γ(z), derived from the entropic gradient of the spin network’s effectiveaction, which introduces a friction term in the linear growth equation. Confrontingthe model with Planck 2018 CMB lensing (AL = 1.073 ± 0.091) and weak-lensingsurveys (DES Y6: S8 = 0.791 ± 0.015; KiDS Legacy: S8 = 0.815 ± 0.016) through afull four-parameter MCMC, we find best-fit values ε0 = 0.066, zc = 4.85, n = 2.02,γ0 = 0.31, yielding AL = 0.946 (tension 1.4σ) and S8 = 0.805 (tension 0.95σ withDES Y6 and 0.61σ with KiDS). The two well-constrained parameters, ε0 and n,admit direct microscopic interpretations as the IR/UV spin ratio and the universalcritical exponent of the RG flow, respectively.
Jean-yves Lozac'h (Thu,) studied this question.