Detector Response to Gravitational Wave Polarizations in Gravitational Quantum Field Theory

TL;DR

This work investigates gravitational wave polarization in Gravitational Quantum Field Theory (GQFT) to test gravity beyond General Relativity using polarization fingerprints. It develops a metric-formulation of GQFT with a gravigauge field and derives a model-independent detector response for space-based detectors, enabling sky-polarization mapping. It shows that only three polarizations are observable via geodesic deviation—$+$, $\times$, and $b$ (breathing)—while vector and longitudinal components are non-tidal; a characteristic $b$-mode signature can separate GQFT from GR in specific sky regions and detector arms. The study provides sky maps and arm-specific response insights to guide future detector design and polarization-based tests of gravity with upcoming gravitational wave observatories.

Abstract

We present an analysis of gravitational wave polarization modes within Gravitational Quantum Field Theory (GQFT), a unified theoretical framework reconciling general relativity and quantum field theory. In the six fundamental polarization: two tensors ($+, \times$), two vectors (x, y), and two scalars (breathing, longitudial) modes of gravitational wave, two tensors and breathing are favored by GQFT. Their distinctive detection signatures in space-based interferometers like LISA and Taiji can be verified. Using first-order orbital dynamics in the Solar System Barycenter frame, we identify three novel observational features: (1) characteristic interference patterns between polarization modes, (2) provide a model-independent response function, and (3) sky-position-dependent optimal detection methods. Our approach provides complete sky coverage through polarization mapping while remaining fully compatible with existing mission designs, notably avoiding the need for challenging direct breathing-mode measurements. The results are presented through comprehensive sky maps, offering both theoretical insights into gravitational wave polarization and practical tools for future detectors. This work establishes a new paradigm for testing fundamental gravity theories through their unique polarization fingerprints

Figures (5)

• Figure 1: Response function with sky position $(\theta, \varphi)=(1.65, 2.10)$ radians on arm12, arm13 and arm23, where blue, orange, green, red, purple, and brown correspond to plus, cross, x, y, breathing, and longitudinal responses respectively.
• Figure 2: GW strain response of arm12 to the HM Cancri system at a specific sky location. Left figure: length strain components for plus, cross, and breathing polarization modes. Middle figure: Total strain comparison between GR (mix of plus and cross modes) and GQFT (including all three polarizations). Right figure: Illustrating the relative temporal rate of strain amplitude change predicted by GR and GQFT can serve as a supplementary reference for the middle figure.
• Figure 3: Same as Figure \ref{['dif12']}, showing the gravitational wave response but for arm13.
• Figure 4: Gravitational wave response of arm23, following the same representation as Figure \ref{['dif12']}.
• Figure 5: The subtraction of the maxima and minima ratio between GR and GQFT over the entire sky location, where the color represents the log discrepancy, redder coloring indicates a greater difference, while bluer coloring indicates a smaller difference, where the difference is exponential. Namely, indicates B mode detectable on arm12, arm13 and arm23 respectively.