  Low-energy effective field theories containing a light scalar field are used
extensively in cosmology, but often there is a tension between embedding such
theories in a healthy UV completion and achieving a phenomenologically viable
screening mechanism in the IR. Here, we identify the range of interaction
couplings which allow for a smooth resummation of classical non-linearities
(necessary for kinetic/Vainshtein-type screening), and compare this with the
range allowed by unitarity, causality and locality in the underlying UV theory.
The latter region is identified using positivity bounds on the $2\to2$
scattering amplitude, and in particular by considering scattering about a
non-trivial background for the scalar we are able to place constraints on
interactions at all orders in the field (beyond quartic order). We identify two
classes of theories can both exhibit screening and satisfy existing positivity
bounds, namely scalar-tensor theories of $P(X)$ or quartic Horndeski type in
which the leading interaction contains an odd power of $X$. Finally, for the
quartic DBI Galileon (equivalent to a disformally coupled scalar in the
Einstein frame), the analogous resummation can be performed near two-body
systems and imposing positivity constraints introduces a non-perturbative
ambiguity in the screened scalar profile. These results will guide future
searches for UV complete models which exhibit screening of fifth forces in the
IR.
