We explore cosmological constraints on the sum of the three active neutrino masses M _ { \nu } in the context of dynamical dark energy ( DDE ) models with equation of state ( EoS ) parametrized as a function of redshift z by w ( z ) = w _ { 0 } + w _ { a } z / ( 1 + z ) , and satisfying w ( z ) \geq - 1 for all z .
We make use of Cosmic Microwave Background data from the Planck satellite , Baryon Acoustic Oscillations measurements , and Supernovae Ia luminosity distance measurements , and perform a Bayesian analysis .
We show that , within these models , the bounds on M _ { \nu } do not degrade with respect to those obtained in the \Lambda \mathrm { CDM } case ; in fact the bounds are slightly tighter , despite the enlarged parameter space .
We explain our results based on the observation that , for fixed choices of w _ { 0 } ,w _ { a } such that w ( z ) \geq - 1 ( but not w = -1 for all z ) , the upper limit on M _ { \nu } is tighter than the \Lambda \mathrm { CDM } limit because of the well-known degeneracy between w and M _ { \nu } .
The Bayesian analysis we have carried out then integrates over the possible values of w _ { 0 } - w _ { a } such that w ( z ) \geq - 1 , all of which correspond to tighter limits on M _ { \nu } than the \Lambda \mathrm { CDM } limit .
We find a 95 % credible interval ( C.I . )
upper bound of M _ { \nu } < 0.13 \mathrm { eV } .
This bound can be compared with the 95 % C.I .
upper bounds of M _ { \nu } < 0.16 \mathrm { eV } , obtained within the \Lambda \mathrm { CDM } model , and M _ { \nu } < 0.41 \mathrm { eV } , obtained in a DDE model with arbitrary EoS ( which allows values of w < -1 ) .
Contrary to the results derived for DDE models with arbitrary EoS , we find that a dark energy component with w ( z ) \geq - 1 is unable to alleviate the tension between high-redshift observables and direct measurements of the Hubble constant H _ { 0 } .
Finally , in light of the results of this analysis , we also discuss the implications for DDE models of a possible determination of the neutrino mass ordering by laboratory searches .