Impacts of gravitational-wave standard siren observations from Einstein
  Telescope and Cosmic Explorer on weighing neutrinos in interacting dark
  energy models
  The multi-messenger gravitational-wave (GW) observation for binary neutron
star merger events could provide a rather useful tool to explore the evolution
of the universe. In particular, for the third-generation GW detectors, i.e.,
the Einstein Telescope (ET) and the Cosmic Explorer (CE), proposed to be built
in Europe and the U.S., respectively, lots of GW standard sirens with known
redshifts could be obtained, which would exert great impacts on the
cosmological parameter estimation. The total neutrino mass could be measured by
cosmological observations, but such a measurement is model-dependent and
currently only gives an upper limit. In this work, we wish to investigate
whether the GW standard sirens observed by ET and CE could help improve the
constraint on the neutrino mass, in particular in the interacting dark energy
(IDE) models. We find that the GW standard siren observations from ET and CE
can only slightly improve the constraint on the neutrino mass in the IDE
models, compared to the current limit. The improvements in the IDE models are
weaker than in the standard cosmological model. Although the limit on neutrino
mass can only be slightly updated, the constraints on other cosmological
parameters can be significantly improved by using the GW observations.
