Cosmology is making impressive progress and it is producing stringent bounds on the sum of the neutrino masses Σ, a parameter of great importance for the current laboratory experiments. In this letter, we exploit the potential relevance of the analysis of Palanque-Delabrouille et al. [JCAP 1502[JCAP , 045 (2015] to the neutrinoless double beta decay (0νββ) search. This analysis indicates small values for the lightest neutrino mass, since the authors find Σ < 84 meV at 1σ C. L., and provides a 1σ preference for the normal hierarchy. The allowed values for the Majorana effective mass, probed by 0νββ, turn out to be < 75 meV at 3σ C. L. and lower down to less than 20 meV at 1σ C. L. . If this indication is confirmed, the impact on the 0νββ experiments will be tremendous since the possibility of detecting a signal will be out of the reach of the next generation of experiments.