Inspiral tests of general relativity and waveform geometry

TL;DR

This paper develops a geometric framework to evaluate the robustness of gravitational wave tests of general relativity, revealing how waveform features and deviations can be distinguished or mimic each other.

Contribution

It introduces a universal geometric approach to analyze waveform deviations, improving detection and interpretation of potential GR violations in gravitational wave data.

Findings

Parameterized tests are sensitive to generic deviations in waveforms.

Waveform geometry governs Bayes factors and biases.

Orthogonal templates help identify degeneracies and enhance deviation detection.

Abstract

The phase evolution of gravitational waves encodes critical information about the orbital dynamics of binary systems. In this work, we test the robustness of parameterized tests against unmodeled deviations from general relativity. We demonstrate that these parameterized tests are flexible and sensitive in detecting generic deviations in the waveform using the Cutler-Vallisneri bias formalism. This universality arises from examining the inherent geometry of the waveform signal and understanding how biases manifest. We show how Bayes factors are governed by the intrinsic geometry of the waveform signal manifold when parameterized tests are used to approximate generic violations of GR. We use the singular value decomposition to propose templates that are orthogonal to parameterized tests, identifying degeneracies and enhancing the detection of potential deviations. More broadly, the geometric framework developed here clarifies -- at a fundamental level -- how subtle waveform effects (including orbital eccentricity, spin precession, waveform systematics, and instrumental glitches) can mimic one another in data, and when they are intrinsically distinguishable.