Consistency and Falsifiability of Screened Scalar Scenarios for Varying Fundamental Constants

Scenarios in which light scalar fields drive both late-time cosmic acceleration and variations of fundamental constants face a well-known tension between cosmological dynamics and stringent local constraints. Screening mechanisms provide a conservative resolution, but their viability depends on a network of internal consistency conditions linking astrophysical, laboratory, and cosmological observations. This article delineates the minimal set of observational requirements that screened scalar scenarios must satisfy, and identifies classes of measurements that would falsify the entire framework in a model-independent manner. By focusing on consistency relations and null tests rather than on specific realizations, we provide a clear and testable benchmark for interpreting current and future searches for varying fundamental constants.