Tests of an EP-Preserving Wake Force

Abstract

A universal quadratic coupling of ultralight scalar dark matter to ordinary matter preserves the weak equivalence principle for unscreened point particles. A finite test body is nevertheless not a passive probe: it distorts the scalar field that accelerates it. We show that this field distortion produces a differential acceleration between concentric test masses, even when their microscopic coupling is universal. We calculate this signal including how each test mass distorts the field acting on the other, deriving the weak-screening limit and extending the calculation to stronger screening using concentric spherical layers. Applying the model to MICROSCOPE, we find differential signals in both its equivalence-principle sensor SUEP, whose test masses have different compositions, and its reference sensor SUREF, whose test masses have the same composition. We combine both sensors with the dark matter wake near Earth to recast the published MICROSCOPE measurements. Within this model, existing measurements probe scalar masses up to approximately $8 \times 10^{-9}\,$eV and couplings below the supernova bound. An analysis using the additional frequency components of the scalar signal could extend the mass reach and probe couplings below the BBN bound.