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Description
Multimessenger gravitational-wave observations provide a powerful probe of fundamental gravity in the strong-field and dynamical regime. In this work, we test possible deviations from general relativity from two complementary perspectives: a temporal variation of the gravitational constant, which is closely related to the strong equivalence principle, and the existence of hidden compact extra dimensions inspired by the Kaluza-Klein formulism. We first develop a gravitational-wave waveform model with a slowly varying gravitational constant, including its effects on both compact binary dynamics and wave propagation in an expanding universe. Applying this framework to GW170817, together with electromagnetic information from GRB 170817A, we obtain no evidence for a varying gravitational constant and constrain \dot{G}/G to [-3.36 × 10^{-9}, 5.34 × 10^{-10}] yr^{-1}. We further use GW170817 to place bounds on hidden extra dimensions and forecast the capability of the future Taiji detector. Representative multimessenger supermassive black hole binaries observed by Taiji are expected to provide significantly stronger constraints, demonstrating the potential of future space-based gravitational-wave astronomy for testing gravity beyond four dimensions.