Equivalence Principle Extension: Universal Non-Minimal Matter–Metric Coupling

The weak equivalence principle is traditionally stated as universal gravitational free fall, tested by composition-dependent experiments to fractional precision 10^-15. In minimally coupled point-particle limits this is closely related to universal kinetic propagation, but canonical normalization is not itself an empirical equivalence principle. EPE asks whether universality extends to the next matter-metric EFT operator: at a specified matching scale, xi in xi R|Phi|^2 is universal across elementary scalar species. EPE fixes the universality of this leading coefficient at mu_star, not its magnitude. At first curvature-response order, EPE supplies three relations: a mass-weighted, species-invariant Ricci phase for elementary scalars; the matched laboratory null Q_B Delta phiA,R - Q_A Delta phiB,R = 0 using Higgs-response charges; and an inflationary spectator effective-mass relation. Within the Standard Model, the laboratory relation is only a consistency null of the Higgs-only first-order matched EFT; it does not by itself compare two elementary scalar sectors. The benchmark xi ~ 10^4 is a conditional magnitude prior motivated by Higgs-inflation nonminimal couplings, not a prediction of EPE alone. The coordinate xi = 1/6 is distinguished by the displayed one-loop beta-function form; beyond one loop, the beta-function zero and RG-invariant trajectory are scheme- and coupling-dependent. Model-dependent CMB+BAO tension in standard Higgs inflation does not directly constrain a universal spectator xi. Empirically, the Ricci phase is formal; matter-overlap or source-modulated atom interferometry tests the matched Q_A null; and cosmology provides a one-way scalar-isocurvature falsification channel plus model-dependent axion/PQ consistency tests. Version v60, dated July 23, 2026.