Precisely measuring the Hubble constant and dark energy using only
  gravitational-wave dark sirens
  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 ${\cal O}(10^5)$-${\cal O}(10^6)$ 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 $H_0$ and the constant EoS of dark energy $w$,
respectively; for a two-parameter EoS parametrization of dark energy, the
precision of $w_0$ is $1.4\%$ and the error of $w_a$ 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.
