Binary systems in massive scalar-tensor theories: Next-to-leading order gravitational wave phase from effective field theory

Neutron star binaries and their associated gravitational wave signal facilitate precision tests of General Relativity. Any deviation of the detected gravitational waveform from General Relativity would therefore be a smoking gun signature of new physics, in the form of additional forces, dark matter particles, or extra gravitational degrees of freedom. To be able to probe new theories, precise knowledge of the expected waveform is required. In our work, we consider a generic setup by augmenting General Relativity with an additional, massive scalar field. We then compute the inspiral dynamics of a binary system, for circular orbits, by employing an effective field theoretical approach, while giving a detailed introduction to the computational framework. Finally, we derive the modified TaylorF2 phase of the gravitational wave signal at next-to-leading order in the post-Newtonian expansion, and leading order in the parameters of the scalar sector, such as the scalar charge. As a consequence of our model-agnostic approach, our results are readily adaptable to a plethora of new physics scenarios, including modified gravity theories and scalar dark matter models.