We investigate the impact of spatial curvature, $\Omega_k$, and dynamical dark energy on the cosmological constraints of the neutrino mass sum, $\sum m_\nu$. Using a joint analysis of the latest CMB (Planck and ACT DR6), BAO (DESI DR2) and SNe Ia (DESY5 and DES-Dovekie) datasets, we perform an exploration of the neutrino mass parameter space. To mitigate prior-driven biases near the physical boundary, we implement a symmetric extension wrapper that allows for effective negative masses. We find that the inclusion of spatial curvature significantly modifies the posterior distributions, exhibiting a smooth transition across the $\sum m_\nu = 0$ threshold. In the $\Lambda$CDM + $\Omega_k$ + $\sum m_{ \nu,\mathrm{ eff}}$ framework, we obtain $\sum m_{ \nu,\mathrm{ eff}} = -0.011^{ +0.052}_{ -0.050}$, reducing the tension with the terrestrial lower limit of 0.06 eV from $2.59\sigma$ for the $\Lambda$CDM + $\sum m_{ \nu,\mathrm{ eff}}$ model to $1.17\sigma$. For the most flexible scenario $w_0 w_a$CDM + $\Omega_k$ + $\sum m_{ \nu,\mathrm{ eff}}$, we find $\sum m_{ \nu,\mathrm{ eff}} = -0.07 \pm 0.11$ with a tension of $1.13\sigma$, illustrating how the increased parameter freedom notably degrades the precision of the mass estimate compared to simpler extensions. Our results demonstrate that current cosmological bounds on $\sum m_\nu$ are heavily influenced by boundary effects and geometric degeneracies.
Categories: astro-ph.CO gr-qc hep-th