Neutrinoless double $\beta$ decay, neutrino mass hierarchy, and neutrino   dark matter
  Recently the evidence of the neutrinoless double $\beta$ ($0\nu \beta\beta$) decay has been announced. This means that neutrinos are Majorana particles and their mass hierarchy is forced to inverted mass hierarchy (Type B) or degenerate mass (Type C) patterns in the diagonal basis of charged lepton mass matrix. We estimate the magnitude of $0\nu \beta\beta$ decay in the degenerate neutrinos including the cosmological constraint of neutrino dark matter, since the inverted mass hierarchy pattern always satisfies the cosmological constraint. The absolute value of neutrino mass is constrained by $0\nu \beta\beta$ experiment or cosmology depending on the relative signs (Majorana CP phases) of neutrino masses. 
Naoyuki Haba, Noboru Nakamura, Tomoharu Suzuki