Forecasting the Interaction in Dark Matter-Dark Energy Models with
  Standard Sirens From the Einstein Telescope
  Gravitational Waves (GW's) can determine the luminosity distance of the
progenitor directly from the amplitude of the wave, without assuming any
specific cosmological model. Thus, it can be considered as a standard siren.
The coalescence of binary neutron stars (BNS) or neutron star-black hole pair
(NSBH) can generate GW's as well as the electromagnetic counterpart, which can
be detected in a form of Gamma-Ray Bursts (GRB) and can be used to determine
the redshift of the source. Consequently, such a standard siren can be a very
useful probe to constrain the cosmological parameters. In this work, we
consider an interacting Dark Matter-Dark Energy (DM-DE) model. Assuming some
fiducial values for the parameters of our model, we simulate the luminosity
distance for a "realistic" and "optimistic" GW+GRB events , which can be
detected by the third-generation GW detector Einstein Telescope (ET). Using
these simulated events, we perform a Monte Carlo Markov Chain (MCMC) to
constrain the DM-DE coupling constant and other model parameters in $1\sigma$
and $2\sigma$ confidence levels. We also investigate how GW's can improve the
constraints obtained by current cosmological probes.
