Probing Lorentz-violating scalar forces and dark matter with precision matter and antimatter experiments

We explore a class of Lorentz-violating scalar-field models where the effects of the scalar field on antimatter can be strongly enhanced compared to matter. Non-trivial differences in phenomenology arise for spectroscopy measurements depending on whether the scalar field changes slowly or rapidly on the atomic scale. We highlight opportunities for precision tests in the laboratory including dark matter searches, in particular with spectroscopy and interferometry measurements, as well as certain types of antimatter experiments.