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.