Negative Masses and Spatial Curvature: Alleviating Neutrino Mass Tensions in LambdaCDM and Extended Cosmologies

Abstract

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.

Figures (9)

• Figure 1: Validation of the code implementation for the extrapolation method. (Upper) Comparison of ratios between negative mass scenarios and the massless case; the red line represents the direct application of Eq. (\ref{['Eq:Mnu_eff']}) within CLASS, while the blue line corresponds to the computation performed via the Cobaya get_model() function. (Lower) Posterior contours comparing the baseline case with a positive mass prior, the extrapolation framework restricted to a positive prior, and the full implementation utilizing a negative prior.
• Figure 2: Triangular plot showing the confidence contours for the $\Lambda$CDM+$\sum m_\nu$ (purple) versus the $\Lambda$CDM+$\Omega_k$+$\sum m_\nu$ (green) models. As observed, including curvature as a varying parameter affects $\Omega_m$, causing the associated densities $\Omega_b$, $\Omega_{cdm}$ and $\Omega_\nu$ to be affected as well. The grey dashed line corresponds to the lower bound value $\sum m_\nu = 0.06$ eV.
• Figure 3: Triangular plot showing the confidence contours for $\omega_0\omega_a$CDM+$\sum m_\nu$ (lime) against $\omega_0\omega_a$CDM+$\Omega_k$+$\sum m_\nu$ (brown). No significant shift is observe in the $\Omega_m$ posterior, whereas $\Omega_{c}$ and $\sum m_\nu$ show a slight sensitivity to the inclusion of curvature, with the effect being more pronounced for the former.
• Figure 4: 2D plot of the $\omega_0$ and $\omega_a$ parameters. It can be observed that the contours for the $\omega_0\omega_a$CDM+$\Omega_k$ and $\omega_0\omega_a$CDM+$\Omega_k$+$\sum m_\nu$ models are nearly identical, while showing a significant difference from $\omega_0\omega_a$CDM+$\sum m_\nu$; this clearly indicates that the shift is driven entirely by curvature. However, the $68\%$ C.L. contour is quite similar across the three models, with the statistical deviation becoming apparent at the $95\%$ C.L., as clearly shown in Figure \ref{['fig:CPL_Pos_tri']}.
• Figure 5: (Upper) 1D posterior distribution for $\sum m_\nu$ across different models. (Lower) 1D posterior distribution for $\Omega_k$ across different models. The vertical dashed lines indicate $\sum m_\nu =0.06$ eV and $\Omega_k=0$, respectively.