Thawing Dark Energy and Massive Neutrinos in Light of DESI

Recent analyses have shown that a dynamic dark energy modeled by the CPL parameterization of the dark energy equation of state (EoS) can ease constraints on the total neutrino mass compared to the standard $\Lambda$CDM model. This helps reconcile cosmological and particle physics measurements of $\sum m_\nu$. In this study, we investigate the robustness of this effect by assessing the extent to which the CPL assumption influences the results. We examine how alternative EoS parameterizations - such as Barboza-Alcaniz (BA), Jassal-Bagla-Padmanabhan (JBP), and a physically motivated thawing parameterization that reproduces the behavior of various scalar field models - affect estimates of $\sum m_\nu$. Although both the BA and JBP parameterizations relax the constraints similarly to the CPL model, the JBP parameterization still excludes the inverted neutrino mass hierarchy at $\sim 2.1\;\sigma$ with $\sum m_\nu < 0.096$\;eV. The thawing parameterization excludes the inverted hierarchy at $\sim 3.3\sigma$ and yields tighter constraints, comparable to those of the $\Lambda$CDM model, with $\sum m_\nu < 0.071$\;eV. Finally, we show that the thawing model can be mapped into the BA and JBP $w_0$-$w_a$ parameter space, with the apparent preference for the phantom regime actually supporting quintessence (non-phantom) models.