Constraints on the sum of the neutrino masses in dynamical dark energy models with $w(z) \geq -1$ are tighter than those obtained in $\Lambda$CDM

TL;DR

This study shows that in dynamical dark energy models with $w(z) \\geq -1$, constraints on the sum of neutrino masses are actually tighter than in the standard $\\Lambda$CDM model, due to degeneracy effects and Bayesian integration over parameters.

Contribution

It demonstrates that cosmological bounds on neutrino masses are not weakened, but slightly improved, in dynamical dark energy models with $w(z) \\geq -1$, compared to $\\Lambda$CDM.

Findings

95% CL upper bound on $M_{\nu}$ is 0.13 eV in $w(z) \\geq -1$ models.

Bounds are tighter than in $\\Lambda$CDM despite larger parameter space.

Dark energy with $w(z) \\geq -1$ does not resolve the Hubble tension.

Abstract

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 perform a Bayesian analysis and show that, within these models, the bounds on $M_{\nu}$ \textit{do not degrade} with respect to those obtained in the $\Lambda$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 $\Lambda$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 $\Lambda$CDM limit. We find a 95\% confidence level (C.L.) upper bound of $M_{\nu}<0.13\,\mathrm{eV}$. This bound can be compared with $M_{\nu}<0.16\,\mathrm{eV}$ at 95\%~C.L., obtained within the $\Lambda$CDM model, and $M_{\nu}<0.41\,\mathrm{eV}$ 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)