Constraints on chameleon gravity from the measurement of the electrostatic stiffness of the $MICROSCOPE$ mission accelerometers

Abstract : This article is dedicated to the use the MICROSCOPE mission’s data to test chameleon theory of gravity. We take advantage of the technical sessions aimed to characterize the electrostatic stiffness of MICROSCOPE’s instrument intrinsic to its capacitive measurement system. Any discrepancy between the expected and measured stiffness may result from unaccounted-for contributors, i.e., extra forces. This work considers the case of chameleon gravity as a possible contributor. It was previously shown that, in situations similar to these measurement sessions, a chameleon fifth force appears and acts as a stiffness for small displacements. The magnitude of this new component of the stiffness is computed over the chameleon’s parameter space. It allows us to derive constraints by excluding any force inconsistent with the MICROSCOPE data. As expected—since MICROSCOPE was not designed for the purpose of such an analysis—these new bounds are not competitive with state-of-the-art constraints, but they could be improved by a better estimation of all effects at play in these sessions. Hence, our work illustrates this novel technique as a new way of constraining fifth forces.