Constraints on the sum of the neutrino masses in dynamical dark energy models with $w(z) \geq -1$ are tighter than those obtained in $Λ$CDM
We explore cosmological constraints on the sum of the three active neutrino masses $M_ν$ 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 perform a Bayesian analysis and show that, within these models, the bounds on $M_ν$ \textit{do not degrade} with respect to those obtained in the $Λ$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 $M_ν$ is tighter than the $Λ$CDM limit because of the well-known degeneracy between $w$ and $M_ν$. 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 $M_ν$ than the $Λ$CDM limit. We find a 95\% confidence level (C.L.) upper bound of $M_ν<0.13\,\mathrm{eV}$. This bound can be compared with $M_ν<0.16\,\mathrm{eV}$ at 95\%~C.L., obtained within the $Λ$CDM model, and $M_ν<0.41\,\mathrm{eV}$ at 95\%~C.L., 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 hierarchy by laboratory searches. (abstract abridged)