On the construction of asymptotically flat initial data in scalar-tensor effective field theory

TL;DR

This paper extends initial data construction methods from General Relativity to scalar-tensor effective field theories with up to four derivatives, demonstrating the existence and uniqueness of solutions under weak coupling conditions.

Contribution

It generalizes the conformal methods for initial data to scalar-tensor theories with higher derivatives, including a Bowen-York type solution.

Findings

Unique solutions exist for the elliptic boundary value problems in weakly coupled regimes.

Standard initial data methods from General Relativity are applicable with minimal modifications.

A generalized Bowen-York solution is derived for these theories.

Abstract

We study the constraint equations for a class of scalar-tensor effective field theories of gravity, including the operators up to $4$ derivatives in the action ($4\partial$ST). We extend the conformal transverse traceless and conformal thin sandwich methods of General Relativity to rewrite the constraint equations of the scalar-tensor theory as a set of elliptic partial differential equations. It is shown that, at weak coupling, a unique solution exists to the corresponding elliptic boundary value problems on asymptotically Euclidean initial slices under similar conditions as in the case of General Relativity. Furthermore, we find a generalization of the Bowen-York solution for $4\partial$ST theories, too. These results demonstrate that standard methods for constructing initial data in General Relativity are applicable (with minimal modification) to weakly coupled $4\partial$ST theories.