Testing the Polarization of Gravitational-wave Background with the LISA-TianQin Network

While general relativity predicts only two tensor modes for gravitational-wave (GW) polarization, general metric theories of gravity allow for up to four additional modes, including two vector and two scalar modes. Observing the polarization modes of GWs could provide a direct test of the modified gravity. The stochastic GW background (SGWB), which can be detected by space-based laser-interferometric detectors at design sensitivity, will provide an opportunity to directly measure alternative polarization. In this paper, we investigate the performance of the LISA-TianQin network for detecting alternative polarizations of stochastic backgrounds, and propose a method to separate different polarization modes. First, we generalize the small antenna approximation to compute the overlap reduction functions for the SGWB with arbitrary polarization, which is suitable for any time-delay interferometry combination. Then we analyze the detection capability of LISA-TianQin for the SGWB with different polarizations. Based on the orbital characteristics of LISA-TianQin, we propose a method to distinguish different polarization modes from their mixed data. Finally, simulation tests are performed to verify the effectiveness of the method. The results of the simulations demonstrate that LISA-TianQin, when employing our proposed method, has the ability to differentiate between various polarization modes, with a specific emphasis on the ability to distinguish between the breathing and longitudinal modes.