We present a unified scalar–tensor framework in which a light dilaton-like field controls both late-time dark energy and the cosmological variation of gauge and Yukawa couplings. Environmental screening suppresses local fifth forces while allowing cosmological evolution. The theory predicts a distinctive two-term redshift dependence of the fine-structure constant, Δα/α (z) = ζα ln (1 + z) + κ (1 + z) ^ (-3/2) − 1, together with a rigid correlation between the variations of α and the proton-to-electron mass ratio μ. Using the observed dark-energy density and the grand-unification scale, we derive benchmark values ζα ≃ −10⁻⁷ and κ ≃ (0. 1–1) × 10⁻⁷, implying a characteristic curvature of Δα/α (z) at redshifts z ≃ 2–3 detectable by ELT/ANDES and molecular absorption systems.
Muñoz Vicedo (Fri,) studied this question.