Semi-agnostic inspiral modeling: the massless scalar case at leading post-Newtonian order

We introduce a semi-agnostic modeling framework for black hole binary inspirals beyond general relativity that fixes the field content without selecting a particular theory. We expand in the post-Newtonian order and in powers of $l/L$, where $l$ is the characteristic length-scale that controls deviations from General Relativity and $L$ is the characteristic length-scale of the system. We focus on the case of a massless scalar field coupled with the metric, at leading post-Newtonian order. Taking into account the scaling with $l/L$ of both the interaction terms and the quantities that characterise the sources, we find that the inspiral can be described in terms of a small number of universal parameters. Such a parametrisation is suitable for obtaining combined bounds from multiple sources and performing searches for specific fields.