Gravitational Wave Polarization Detection with Pyramid Constellation of Gravitational Wave Observatory

In general relativity (GR), gravitational wave (GW) polarization modes are tensor named as plus and cross modes, which have been detected from the LIGO, Virgo, and KAGRA collaborations. The other GW modes beyond GR, called as two scalar polarization modes and two vector modes, have being probed especially with an expected network of Advanced LIGO, Advanced Virgo, and KAGRA. For the space-based GW detection, the LISA - Taiji networks can perform the detection of GW polarizations. For the first time, we have come up with the pyramid constellation of gravitational wave observatory(PCGO) for GW polarization detection. The configuration of PCGO can be simultaneously sensitive to the six polarization modes of GWs. The response intensity of six detector arms changes with the detector positions on orbit in one year period. The newly added three arms have a different response of GWs from the triangle arms, comparing to LISA, Taiji and Tianqin. That indicates that there are more freedoms for the polarization component extraction from the total polarization signals of GWs. Comparing to LISA, Taiji and Tianqin configuration, PCGO has more combinations of optical paths of time delay interferometer (TDI) to suppress the frequency noise. The unequal arm Michelson TDI configuration and the Sagnac TDI configuration are equally effective for elimination of the laser frequency noise.