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Using the self-force approach, we present the premier first-post-adiabaticaccuracy formalism for modelling compact binaries in theories with a masslessscalar field non-minimally coupled to gravity. We limit the binary secondary tobeing a non-spinning compact body with no scalar dipole (we will address thespinning and scalar dipole cases in an upcoming paper). By producing an ansatzfor the scalar charged point particle action, we derive first- and second-orderperturbative field equations and equations of motion for the secondary compactobject. Under our assumptions, implementing this formalism will producesufficiently accurate waveform templates for precision measurements of thescalar charge of the secondary with LISA data on extreme-mass-ratio inspirals.Our formalism is consistent with almost general scalar-tensor theories ofgravity. Implementing our formalism builds on self-force models in GeneralRelativity; we show the incorporation into the two-timescale formalism isstraightforward. Excitingly, implementation poses no significantly morechallenging barriers than computing first-post adiabatic waveforms in GeneralRelativity.

Measuring scalar charge with compact binaries: High accuracy modelling with self-force