Equivalence-Principle Tests and Dark-Matter Constraints in Symmergent Gravity

We investigate whether the low-energy gravitational sector of symmergence can produce observable violations of the universality of free fall or account for dark-matter phenomenology. The quadratic-curvature term introduces a scalar degree of freedom, but its coupling through the Jordan-frame metric is universal and therefore does not by itself generate composition-dependent acceleration. Such a signal requires nonuniversal curvature sensitivities of composite masses. We derive the exterior curvature profile of a finite spherical source and apply it to the Earth and the MICROSCOPE titanium and platinum test masses. Matching the effective sensitivities to the symmergent Higgs–curvature interaction gives a maximum differential-acceleration signal of approximately 1.83 × 10 −53 , far below the MICROSCOPE sensitivity. The scalaron range that formally maximizes this signal would require a fermion–boson degree-of-freedom imbalance of order 10 83 and is independently excluded by universal fifth-force constraints. Particle spectra of conventional size instead give a formal microscopic pole, often above the low-energy cutoff. We also show that the fixed-strength Yukawa correction of the minimal quadratic-curvature sector cannot replace a galactic dark-matter halo because, after calibrating the locally measured Newton constant, it weakens rather than enhances the outer force, remains Keplerian, and does not enhance the linearized lensing potential. Current equivalence-principle experiments therefore do not test the minimal symmergent Higgs channel, but they can constrain additional nonuniversal curvature-dependent operators within a consistently specified effective theory.