Model-Independent Test of General Relativity: An Extended post-Einsteinian Framework with Complete Polarization Content

TL;DR

This paper introduces a comprehensive, model-independent framework to test General Relativity using gravitational wave data, accounting for all possible polarizations and enabling constraints on alternative gravity theories.

Contribution

It develops an extended parameterized post-Einsteinian template family that includes complete polarization content, improving the ability to detect deviations from General Relativity in gravitational wave signals.

Findings

The framework can distinguish between GR and alternative theories with additional polarizations.

It provides a method to constrain new polarization parameters using multiple detector data.

The template family reduces to GR predictions when new parameters are set to specific values.

Abstract

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.