Correlated Cosmological Variations of Fundamental Constants from a Screened Unified Scalar Field

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 the fine-structure constant 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 that is detectable by next-generation spectroscopic facilities such as ELT/ANDES and by molecular absorption systems.