Probing gravitational quantum field theory through polarization fingerprints of gravitational waves

Abstract

Gravitational quantum field theory (GQFT) has been proposed as a candidate framework to reconcile general relativity with quantum field theory, and a distinctive imprint on gravitational-wave (GW) polarizations is crucially predicted. While general relativity allows only two tensor modes (+, ×), GQFT additionally favors a massless breathing scalar mode, providing a compelling yet largely unexplored observational target for testing quantum gravity. The central challenge is therefore to assess, in a mission-agnostic manner, how well future space-based interferometers can disentangle and detect these tensor and scalar polarization components across the sky. In this work, we develop a model-independent response formalism for LISA- and Taiji-like detectors by incorporating first-order orbital dynamics in the solar system barycenter frame. This framework yields three key observational consequences: (i) characteristic interference patterns between tensor and scalar modes, (ii) a generalized, model-independent response function for the breathing mode, and (iii) sky-position-dependent strategies that optimize detectability. We further translate the formalism into comprehensive polarization maps that provide complete sky coverage and remain fully compatible with existing mission designs, thereby circumventing the need for challenging direct breathing-mode measurements. Overall, our results deliver practical tools for future data analysis and establish a systematic avenue to test fundamental theories of gravity through their GW polarization fingerprints.