Constraining Screened Modified Gravity by Space-borne Gravitational-wave Detectors

The screened modified gravity (SMG) is a unified theoretical framework, which describes the scalar-tensor gravity with screening mechanism. Based on the gravitational-wave (GW) waveform derived in our previous work \citep{liu2018waveforms}, in this article we investigate the potential constraints on SMG theory through the GW observation of the future space-borne GW detectors, including LISA, TianQin and Taiji. We find that, for the EMRIs consisting of a massive black hole and a neutron star, if the EMRIs are at Virgo cluster, the GW signals can be detected by the detectors at quite high significant level, and the screened parameter $\epsilon_{\rm NS}$ can be constrained at about $\mathcal{O}(10^{-5})$, which is more than one order of magnitude tighter than the potential constraint given by ground-based Einstein telescope. However, for the EMRIs consisting of a massive black hole and a white dwarf, it is more difficult to be detected than the previous case. For the specific SMG models, including chameleon, symmetron and dilaton, we find these constraints are complementary with that from Cassini experiment, but weaker than those from lunar laser ranging observations and binary pulsars, due to the strong gravitational potentials on the surface of neutron stars. By analyzing the deviation of GW waveform in SMG from that in general relativity, as anticipated, we find the dominant contribution of the SMG constraining comes from the correction terms in the GW phases, rather than the extra polarization modes or the correction terms in the GW amplitudes.