Constraint on gravitational-wave polarizations for space-based detectors with time-delay interferometry

Abstract Probing extra polarizations in gravitational waves (GWs) with space-based detectors is the most direct method for testing theories of gravity. In this paper, by employing the second-generation time-delay interferometry (TDI) to cancel out the laser frequency noise in a rotating and flexing configuration with arm lengths varying linearly in time, and using the parametrized post-Einstein (ppE) waveform, we study the detectors’ constraint ability on extra polarizations, and explore the impacts of TDI on the constraint of polarizations. We find that the constraints on extra polarizations are significantly weaker than the tensor mode, especially for the scalar breathing and scalar longitudinal modes. However, the detectability improves with increasing gravitational-wave source mass for the vector mode. Since the detector’s capability to constrain polarizations depends mainly on the signal-to-noise ratio (SNR), it has minimal impact on the SNR when applying the TDI method to the signal response. Therefore, the use of the TDI method does not significantly affect the extra polarization constraints in practical GW detection.