Accurate Computation of the Screening of Scalar Fifth Forces in Galaxies

Screening mechanisms allow light scalar fields to dynamically avoid the constraints that come from our lack of observation of a long-range fifth force. Galactic scale tests are of particular interest when the light scalar is introduced to explain the dark matter or dark energy that dominates our cosmology. To date, much of the literature that has studied screening in galaxies has described screening using simplifying approximations. In this work, we calculate numerical solutions for scalar fields with screening mechanisms in galactic contexts, and use these to derive new, precise conditions governing where fifth forces are screened. We show that the commonly used binary screened/unscreened threshold can predict a fifth force signal in situations where a fuller treatment does not, leading us to conclude that existing constraints might be significantly overestimated. We show that various other approximations of the screening radius provide a more accurate proxy to screening, although they fail to exactly reproduce the true screening surface in certain regions of parameter space. As a demonstration of our scheme, we apply it to an idealised Milky Way and thus identify the region of parameter space in which the solar system is screened.