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, eff framework, we obtain sum m ν, 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, eff model to 1.17σ. For the most flexible scenario w 0 w a CDM + Ω k + sum m ν, eff, we find sum m ν, eff = -0.07 plus or minus 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.