  Relaxing the conventional assumption of a minimal coupling between the dark
matter (DM) and dark energy (DE) fields introduces significant changes in the
predicted evolution of the Universe. Therefore, testing such a possibility
constitutes an essential task not only for cosmology but also for fundamental
physics. In a previous communication [Phys. Rev. D99, 043521, 2019], we
proposed a new null test for the $\Lambda$CDM model based on the time
dependence of the ratio between the DM and DE energy densities which is also
able to detect potential signatures of interaction between the dark components.
In this work, we extend that analysis avoiding the $ \Lambda$CDM assumption and
reconstruct the interaction in the dark sector in a fully model-independent way
using data from type Ia supernovae, cosmic chronometers and baryonic acoustic
oscillations. According to our analysis, the $\Lambda$CDM model is consistent
with our model-independent approach at least at $3\sigma$ CL over the entire
range of redshift studied. On the other hand, our analysis shows that the
current background data do not allow us to rule out the existence of an
interaction in the dark sector. Finally, we present a forecast for
next-generation LSS surveys. In particular, we show that Euclid and SKA will be
able to distinguish interacting models with about 4\% of precision at $z\approx
1$.
