Scalar Fields Near Compact Objects: Resummation versus UV Completion

TL;DR

This paper investigates the conditions under which scalar field theories near compact objects can be resummed for screening mechanisms, comparing these with UV consistency bounds, and identifies classes of theories compatible with both.

Contribution

It characterizes the interaction couplings allowing classical resummation for screening and compares them with UV bounds from unitarity, causality, and positivity constraints.

Findings

Scalar-tensor theories with odd powers of X can exhibit screening and satisfy positivity bounds.

Resummation near two-body systems for quartic DBI Galileon reveals non-perturbative ambiguities.

Positivity bounds constrain interactions at all orders, guiding UV complete model development.

Abstract

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.