Model-independent test of general relativity: An extended post-Einsteinian framework with complete polarization content

We develop a model-independent test of general relativity that allows for the constraint of the gravitational wave (GW) polarization content with GW detections of binary compact object inspirals. We first consider three modified gravity theories (Brans-Dicke theory, Rosen's theory, and Lightman-Lee theory) and calculate the response function of ground-based detectors to gravitational waves in the inspiral phase. This allows us to see how additional polarizations predicted in these theories modify the general relativistic prediction of the response function. We then consider general power-law modifications to the Hamiltonian and radiation-reaction force and study how these modify the time-domain and Fourier response function when all polarizations are present. From these general arguments and specific modified gravity examples, we infer an improved parameterized post-Einsteinian template family with complete polarization content. This family enhances general relativity templates through the inclusion of new theory parameters, reducing to the former when these parameters acquire certain values, and recovering modified gravity predictions for other values, including all polarizations. We conclude by discussing detection strategies to constrain these new, polarization theory parameters by constructing certain null channels through the combination of output from multiple detectors.