Negative Masses and Spatial Curvature: Effects on the neutrino mass tension in LambdaCDM and extended cosmologies
We investigate the impact of spatial curvature, $Ω_k$, and dynamical dark energy on the cosmological constraints of the neutrino mass sum, $\sum m_ν$. 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 $\sum m_ν= 0$ threshold. In the $Λ$CDM + $Ω_k$ + $\sum m_{ν,\mathrm{eff}}$ framework, we obtain $\sum m_{ν,\mathrm{eff}} = -0.011^{+0.052}_{-0.050}$, reducing the tension with the terrestrial lower limit of 0.06 eV from $2.59σ$ for the $Λ$CDM + $\sum m_{ν,\mathrm{eff}}$ model to $1.17σ$. For the most flexible scenario $w_0 w_a$CDM + $Ω_k$ + $\sum m_{ν,\mathrm{eff}}$, we find $\sum m_{ν,\mathrm{eff}} = -0.07 \pm 0.11$ with a tension of $1.13σ$, 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 $\sum m_ν$ are heavily influenced by boundary effects and geometric degeneracies.