Constraining almost degenerate three-flavor neutrinos

We discuss constraints on a scenario of almost degenerate three-flavor neutrinos imposed by the solar and the atmospheric neutrino anomalies, hot dark matter, and in particular by the neutrinoless double $\beta$ decay experiments. It is found that in the Majorana version of the model the region with relatively large ${\theta }_{13}$ is favored and the model is not compatible with the popular small-${\theta }_{12}$ Mikheyev-Smirnov-Wolfenstein solution of the solar neutrino problem. A constraint on the $\mathrm{CP}$-violating phases including the one characteristic to Majorana neutrinos is also obtained. The stability of our conclusion against the uncertainty of the nuclear matrix elements of double $\beta$ decay is briefly addressed.