Algebraic Bounds on Chameleon Screening and Implications for Satellite Tests of Gravity

This work derives algebraic bounds on perturbative control in chameleon-type scalar–tensor screening models and examines their implications for satellite tests of the Weak Equivalence Principle. Starting from the Jordan-frame action with an exponential conformal coupling, the analysis obtains the static field equation and the density-dependent minimum of the effective potential in closed form using the Lambert-W function. The resulting expressions link microscopic coupling parameters to macroscopic thin-shell observables. When evaluated using fiducial parameters relevant to the MICROSCOPE satellite experiment, the bare scalar signal exceeds the experimental bound unless strong environmental screening occurs in the Earth–satellite system. The results isolate a regime in which detectability of screened scalar forces is controlled primarily by terrestrial environmental screening rather than by laboratory-scale perturbative limits.