Testing alternative theories of gravity with space-based gravitational wave detectors

We use gravitational waves (GWs) from binary black holes (BBHs) and neutron stars inspiralling into intermediate-mass black holes to evaluate how accurately the future space-based GW detectors such as LISA, Taiji and TianQin and their combined networks can determine source parameters and constrain alternative theories of gravity. We find that compared with single detector, the detector network can greatly improve the estimation errors of source parameters, especially the sky localization, but the improvement of the constraint on the graviton mass $m_g$ and the Brans-Dicke coupling constant $\omega_{BD}$ is small. We also consider possible scalar modes existed in alternative theories of gravity and we find the inclusion of the scalar mode has little effect on the constraints on source parameters, $m_g$, and $\omega_{BD}$ and the parameterized amplitude $A_B$ of scalar modes is small. % delete is small? For the constraint on the graviton mass, we consider both the effects in the GW phase and the transfer function due to the mass of graviton. % in both, delete due to ...? With the network of LISA, Taiji and TianQin, we get the lower bound on the graviton Compton wavelength $\lambda_g\gtrsim 1.24 \times 10^{20}$ m for BBHs with masses $(10^6+10^7)M_\odot$, and $A_B< 1.6\times 10^{-4}$ for BBHs with masses $(1+2)\times 10^5M_\odot$; $\omega_{BD}>6.12\times10^{6}$ and $A_B< 8.21\times10^{-3}$ for neutron star-black hole binary with masses $(1.4+400)M_{\odot}$.