Coupling between cold dark matter and dark energy from neutrino mass experiments

We consider cosmological models with dynamical dark energy (dDE) coupled to cold dark matter (CDM), while simultaneously allowing neutrinos to be massive. Using a MCMC approach, we compare these models with a wide range of cosmological data sets. We find a strong correlation between this coupling strength and the neutrino mass. This correlation persists when BAO data are included in the analysis. We add then priors on $\nu$ mass from particle experiments. The claimed detection of $\nu$ mass from the Heidelberg-Moscow neutrinoless double--$\beta$ decay experiment would imply a 7--$8 \sigma$ detection of CDM-DE coupling. Similarly, the detection of $\nu$ mass from coming KATRIN tritium $\beta$ decay experiment will imply a safe detection of a coupling in the dark sector. Previous attempts to accommodate cosmic phenomenology with such possible $\nu$ mass data made recourse to a $w < -1$ eoS. We compare such an option with the coupling option and find that the latter allows a drastic improvement.