Using the measurements of tidal deformations in the binary neutron star (BNS) coalescences can obtain the information of redshifts of gravitational wave (GW) sources, and thus actually the cosmic expansion history can be investigated by solely using such GW dark sirens. To do this, the key is to get large amounts of accurate GW data, which can be achieved by employing the third-generation (3G) GW detectors. In this paper, we wish to offer an answer to the question of whether the Hubble constant and the equation of state (EoS) of dark energy can be precisely measured by solely using GW dark sirens. We find that in the era of 3G GW detectors O(10 5 )-O(10 6 ) dark siren data (with the tidal measurements) can be obtained in a several-year observation, and thus using only dark sirens can actually achieve the precision cosmology. Based on a network of 3G detectors, we obtain the constraint precisions of 0.1% and 0.6% for the Hubble constant H0 and the constant EoS of dark energy w, respectively; for a two-parameter EoS parametrization of dark energy, the precision of w0 is 1.4% and the error of wa is 0.086. We conclude that 3G GW detectors would lead to breakthroughs in solving the Hubble tension and revealing the nature of dark energy.
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