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Neutron star binaries and their associated gravitational wave signalfacilitate precision tests of General Relativity. Any deviation of the detectedgravitational waveform from General Relativity would therefore be a smoking gunsignature of new physics, in the form of additional forces, dark matterparticles, or extra gravitational degrees of freedom. To be able to probe newtheories, precise knowledge of the expected waveform is required. In our work,we consider a generic setup by augmenting General Relativity with anadditional, massive scalar field. We then compute the inspiral dynamics of abinary system by employing an effective field theoretical approach, whilegiving a detailed introduction to the computational framework. Finally, wederive the modified gravitational waveform at next-to-leading order. As aconsequence of our model-agnostic approach, our results are readily adaptableto a plethora of new physics scenarios, including modified gravity theories andscalar dark matter models.

Binary Systems in Massive Scalar-Tensor Theories: Next-to-Leading Order Gravitational Waveform from Effective Field Theory