The Shape Dependence of Vainshtein Screening

Scalar field theories that possess a Vainshtein mechanism are able to dynamically suppress the associated fifth forces in the presence of massive sources through derivative non-linearities. The resulting equations of motion for the scalar are highly non-linear and therefore very few analytic solutions are known. Here we present a brief investigation of the structure of Vainshtein screening in symmetrical configurations, focusing in particular on the spherical, cylindrical and planar solutions that are relevant for observations of the cosmic web. We consider Vainshtein screening in both the Galileon model, where the non-linear terms involve second derivatives of the scalar, and a k-essence theory, where the non-linear terms involve only first derivatives of the scalar. We find that screening, and consequently the suppression of the scalar force, is most efficient around spherical sources, weaker around cylindrical sources and can be absent altogether around planar sources.