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Credit: ©Science China Press The Hubble parameter is one of the central parameters in the modern cosmology. Their values inferred from the late-time observations are systematically higher than those from the early-time measurements by about 10%. This is called the Hubble tension . To come to a robust conclusion, independent probes with accuracy at percent levels are crucial. With the self-calibration by the theory of general relativity, gravitational waves from compact binary coalescence open a completely novel observational window for Hubble parameter determination. Hence, it can shed some light on the Hubble tension. Depends on whether being associated with electromagnetic counterparts or not, gravitational wave events can be categorized into bright sirens and dark sirens. The future space-borne gravitational wave observatory network, such as the LISA-Taiji network, will be able to measure the gravitational wave signals in the Millihertz bands with unprecedented accuracy. This a

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