Matter-Wave Interferometry Tests of Density Field Dynamics

Density Field Dynamics (DFD) posits a scalar refractive field ψ(x) such that light propagates with n=e^ψ (one-way phase speed c₁=ce^(-ψ)) and matter accelerates as a=c²∇ψ/2. While cavity-atom redshift tests probe the photon sector, matter-wave interferometers test the external wavefunction coupling. We derive the perturbative phase from the ∇ψ·∇ operator in the DFD-modified Schrödinger equation and obtain a clean discriminator for light-pulse interferometers: Δφ_DFD = (ℏk_eff²/m)(g/c²)T³, in contrast to the standard GR scaling Δφ_GR = k_eff g T². We provide explicit predictions for Kasevich-Chu, Raman, and Bragg geometries (vertical and horizontal), source-mass configurations, and dual-species protocols (Rb/Yb), and analyze systematics with look-alike time scalings. For Earth g and k_eff~1.6×10⁷ m⁻¹ (Rb, 780 nm), the DFD residual is ~2×10⁻¹¹ rad at T=1s, within reach of current long-baseline instruments using rotation, k-reversal, and source-mass modulation.