Searching for Chameleon Dark Energy with Mechanical Systems

We consider using optically levitated microspheres and torsion balances as screened scalar field detectors. We present a novel derivation for the classical chameleon force between two spherical bodies which remains valid at smaller separation distances and stronger chameleon couplings than previous work. Using this and experimental sensitivities achieved by the current generation of experiments, we show predicted constraints on chameleons as dark energy. We include analytic expressions for the parameter space that can be probed by future experiments in terms of experimental parameters. We also indicate regions of theoretically well-motivated chameleon parameter space which should be the aim for future experiments.