Inspiral tests of general relativity and waveform geometry

The phase evolution of gravitational waves encodes critical information about the orbital dynamics of binary systems. In this work, we test the robustness of post-Newtonian coefficients against unmodeled deviations from general relativity. We demonstrate that the parameterized tests are flexible and sensitive in detecting generic deviations in the waveform. This universality arises from examining the inherent geometry of the waveform signal and understanding how biases manifest. We propose templates that are orthogonal to parameterized tests, avoiding degeneracies and enhancing the detection of potential deviations. This framework also provides insights into when it is easier to distinguish between orbital eccentricity and spin-induced precession.