The Scalar-Imprint Field: Phenomenological Constraints and the Cosmological Drift of Newton's Constant

We propose that the organizing degree of freedom underlying binary physical distinguishability manifests cosmologically as a scalar-imprint field Φ whose evolution modulates the effective gravitational coupling Geff. Adopting the exponential coupling F(Φ) = eβGΦ, motivated by the Damour–Polyakov least-coupling principle, we write a scalar-tensor action in which Gis a dynamical variable. Variation of the action yields complete, closed-form modified Einstein equations and a scalar equation of motion. We define the dimensionless drift parameter λ≡dln G/dln a and show ˙ it is related to the field’s slow-roll velocity and coupling strength by λ=−βG Φ/H. Benchmarking against Lunar Laser Ranging (LLR) constrains |λ|≲3.2 ×10−5 , consistent with the sector-saturation suppression λ= κ/17 derived in the companion paper. We also show that gauge couplings evolve proportionally to G, giving ˙ ˙ αi/αi = (βi/βG) G/G, a second independent observable consequence. The framework is fully consistent with ΛCDM at current precision while predicting measurable deviations at next-generation experimental sensitivity.