Prospects for gravitational-wave polarization test from compact binary mergers with future ground-based detectors

There exist six possible polarization modes of gravitational waves in general metric theory of gravity, while two tensor polarization modes are allowed in general relativity. The properties and number of polarization modes depend on gravity theories. The number of the detectors needs to be equal to the number of the polarization modes of the gravitational waves for separation of polarizations basically. However, a single detector having great sensitivity at lower frequency could be effectively regarded as a virtual detector network including a set of detectors along its trajectory due to a long GW signal from a compact binary and the Earth's rotation. Thus, time-varying antenna pattern functions can help testing the polarizations of gravitational waves. We study the effects of the Earth's rotation on the polarization test and show a possibility to test the non-tensorial polarization modes from future observations of compact binary mergers with ground-based gravitational detectors such as Einstein telescope and Cosmic Explorer.