By introducing two parameterized dark energy models and a dimensionless variable \Delta = ( m _ { 3 } - m _ { 1 } ) / ( m _ { 3 } + m _ { 1 } ) in the range [ -1 , 1 ] , which is used to identify neutrinos mass hierarchy , the total neutrino mass and neutrino mass hierarchy has been studied beyond the \Lambda CDM model .
When the results of neutrino oscillation experiments are considered , the unique hierarchy parameter \Delta determines all the masses of neutrinos , and a positive ( negative ) sign of \Delta describes the normal ( inverted ) mass hierarchy .
The two typical cosmology models considered are w CDM model and w _ { 0 } w _ { a } CDM model .
Adopting the currently available cosmic observations , the models parameter space is scanned via the Markov chain Monte Carlo method , as a comparison to the \Lambda CDM model , the upper limits of the total neutrino mass \sum _ { \nu } m _ { \nu } become looser due to the addition of model parameters for dark energy .
In the w CDM ( w _ { 0 } w _ { a } CDM ) model the total mass of neutrinos is \sum _ { \nu } m _ { \nu } < 0.142 eV ( \sum _ { \nu } m _ { \nu } < 0.179 eV ) for the normal mass hierarchy and \sum _ { \nu } m _ { \nu } < 0.158 eV ( \sum _ { \nu } m _ { \nu } < 0.198 eV ) for the inverted mass hierarchy at 95 \% C.L..
The normal mass hierarchy is slightly favored for the \Lambda CDM model , but this tendency becomes weak for the w CDM model and even disappears for the w _ { 0 } w _ { a } CDM model .