Violation of the equivalence principle from light scalar dark matter

In this paper, we study the local observational consequences of a violation of the Einstein Equivalence Principle induced by models of light scalar Dark Matter (DM). We focus on two different models where the scalar field couples linearly or quadratically to the standard model of matter fields. For both these cases, we derive the solutions of the scalar field. We also derive from first principles the expressions for two types of observables: (i) the local comparison of two atomic sensors that are differently sensitive to the constants of Nature and (ii) the local differential acceleration between two test-masses with different compositions. For the linear coupling, we recover that the signatures induced by DM on both observables are the sum of harmonic and Yukawa terms. For the quadratic coupling on the other hand, the signatures derived for both types of observables turn out to be a sum of a time independent term and of an harmonic oscillation, whose amplitudes both depend on the position. Such a behavior is new and can make experiments in space more sensitive than terrestrial ones. Besides, the observables present some interesting non-linear behaviors that are due to the amplification or to the screening of the scalar-field, depending on the parameters of the theory, and on the compactness of the source of the gravitational field. Finally, we infer the various limits on the DM coupling parameters by using existing frequency comparisons on the one hand and tests of the universality of free fall on the ground (torsion balances) or in space (MICROSCOPE mission) on the other hand. We show that in the quadratic case, so-called natural parameters are still allowed by observations.