Distinguishing gravity theories with networks of space-based gravitational-wave detectors

We propose a method for separating and detecting the non-tensor modes of stochastic gravitational-wave backgrounds (SGWBs) using networks of space-based gravitational-wave detectors. We consider four distinct data-reconstruction schemes for the co-inclination and anti-inclination orbital configurations of the LISA-Taiji network. We find that the co-inclination configuration offers its advantages over the anti-inclination one and can achieve signal-to-noise ratios up to 17.3 for the vector modes and 10.4 for the scalar modes with the energy density spectrum as $Ω_{GW}^p(f)=10^{-12}$. Our method can be used to measure beyond-general-relativity polarization modes of SGWBs at mHz frequency band, opening a new avenue for testing alternative gravity theories.