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

The weak equivalence principle asserts that all matter species couple identically to the spacetime metric at the kinetic-term level, tested by composition-dependent free-fall experiments to fractional precision 10^-15. This paper asks whether that universality stops at the kinetic term or extends to the next operator in the effective-field-theory expansion of the matter–metric interaction. The Equivalence Principle Extension (EPE) is the postulate that it does: at a specified matching scale, the coefficient ξ of the non-minimal curvature operator ξ R |Φ|^2 is universal across elementary scalar species. EPE fixes the universality of this leading coefficient at μ★, not its magnitude.

Three empirical relations carry the content of the postulate at first curvature-response order: (i) for elementary scalars, the Ricci-coupled phase along a common trajectory is mass-weighted and species-invariant; (ii) for ordinary laboratory matter, matching the Standard Model Higgs operator ξ_H R H†H onto atomic rest masses yields the leading laboratory null Q_B Δϕ_{A,R} − Q_A Δϕ_{B,R} = 0 via the Higgs-response charge Q_A; (iii) on an inflationary quasi-de Sitter background, every scalar spectator obeys m_eff^2 = m^2 + 12 ξ ℏ^2 H_inf^2 / c^4. The three relations have different empirical status: the Ricci phase is a formal elementary-scalar relation, differential matter-overlap or source-modulated atom interferometry tests the matched Q_A null, and cosmology supplies a one-way scalar-isocurvature falsification channel together with model-dependent axion/PQ-sector consistency tests.

The manuscript develops the EPE postulate, its laboratory and cosmological empirical channels, the matched effective field theory linking the elementary-scalar operator to composite matter via a Damour–Donoghue decomposition, an open-system Lindblad extension recovering the standard Blencowe gravitational-decoherence rate, and the relation of EPE to the Spacetime Pilot Wave (SPW) hypothesis as one possible ontological reading.

This is the final manuscript version (v59), dated April 27, 2026.