Constraints on the sum of the neutrino masses in dynamical dark energy models with w(z)≥−1 are tighter than those obtained in ΛCDM

We explore cosmological constraints on the sum of the three active neutrino masses ${M}_{\ensuremath{\nu}}$ 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 $w(z)\ensuremath{\ge}\ensuremath{-}1$ for all $z$. We make use of cosmic microwave background data from the Planck satellite, baryon acoustic oscillation measurements, and supernovae Ia luminosity distance measurements, and perform a Bayesian analysis. We show that, within these models, the bounds on ${M}_{\ensuremath{\nu}}$ do not degrade with respect to those obtained in the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ 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 $w(z)\ensuremath{\ge}\ensuremath{-}1$ (but not $w=\ensuremath{-}1$ for all $z$), the upper limit on ${M}_{\ensuremath{\nu}}$ is tighter than the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ limit because of the well-known degeneracy between $w$ and ${M}_{\ensuremath{\nu}}$. The Bayesian analysis we have carried out then integrates over the possible values of ${w}_{0}\text{\ensuremath{-}}{w}_{a}$ such that $w(z)\ensuremath{\ge}\ensuremath{-}1$, all of which correspond to tighter limits on ${M}_{\ensuremath{\nu}}$ than the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ limit. We find a 95% credible interval (C.I.) upper bound of ${M}_{\ensuremath{\nu}}<0.13\text{ }\text{ }\mathrm{eV}$. This bound can be compared with the 95% C.I. upper bounds of ${M}_{\ensuremath{\nu}}<0.16\text{ }\text{ }\mathrm{eV}$, obtained within the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ model, and ${M}_{\ensuremath{\nu}}<0.41\text{ }\text{ }\mathrm{eV}$, obtained in a DDE model with arbitrary EoS (which allows values of $w<\ensuremath{-}1$). Contrary to the results derived for DDE models with arbitrary EoS, we find that a dark energy component with $w(z)\ensuremath{\ge}\ensuremath{-}1$ 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.