Reconstruction of the dark sectors' interaction: A model-independent
  inference and forecast from GW standard sirens
  Interacting dark matter (DM) - dark energy (DE) models have been intensively
investigated in the literature for their ability to fit various data sets as
well as to explain some observational tensions persisting within the
$\Lambda$CDM cosmology. In this work, we employ the Gaussian processes (GP)
algorithm to perform a joint analysis by using the geometrical cosmological
probes such as Cosmic chronometers, Supernova Type Ia, Baryon Acoustic
Oscillations, and the H0LiCOW lenses sample to infer a reconstruction of the
coupling function between the dark components in a general framework, where the
DE can assume a dynamical character via its equation of state. In addition to
the joint analysis with these data, we simulate a catalogue with standard siren
events from binary neutron star mergers, within the sensitivity predicted by
the Einstein Telescope, to reconstruct the dark sector coupling with more
accuracy in a robust way. We find that the particular case, where $w = -1$ is
fixed on the DE nature, has a statistical preference for an interaction in the
dark sector at late times. In the general case, where $w(z)$ is analysed, we
find no evidence for such dark coupling, and the predictions are compatible
with the $\Lambda$CDM paradigm. When the mock events of the standard sirens are
considered to improve the kernel in GP predictions, we find a preference for an
interaction in the dark sector at late times.
