Neutrino mass constraints in the Schwarzschild-de Sitter black-hole dark energy model with ACT DR6 and DESI DR2 data
Recent DESI observations have posed new challenges to $\Lambda$CDM, showing a preference for dynamical dark energy and yielding neutrino mass constraints within $\Lambda$CDM that approach the lower bound allowed by neutrino oscillation experiments. In this work, we investigate cosmological constraints on the key neutrino parameters, $\sum m_\nu$ and $N_{\rm eff}$, within the Schwarzschild-de Sitter black-hole dark energy (SdSDE) framework. We use cosmic microwave background (CMB) data from Planck and ACT DR6, baryon acoustic oscillation data from DESI DR2, and type Ia supernova data from DES-Dovekie and PantheonPlus. We find that SdSDE scenarios prefer a positive neutrino mass whenever $\sum m_\nu$ is allowed to vary. Using CMB+DESI+DES-Dovekie data, we obtain $\sum m_\nu=0.207^{+0.047}_{-0.052}~{\rm eV}$ for SdSDE+$\sum m_\nu$, reduced to $\sum m_\nu=0.162^{+0.055}_{-0.056}~{\rm eV}$ when $N_{\rm eff}$ is also varied. This arises from the positive correlation between $N_{\rm eff}$ and $\sum m_\nu$, together with the systematic preference of SdSDE for values of $N_{\rm eff}$ below the standard value. Furthermore, the best-fit $\chi^2$ comparison shows that $\Lambda$CDM with extended neutrino parameters is strongly preferred over the corresponding SdSDE extension. Overall, the positive neutrino mass preference induced by SdSDE may reflect parameter compensation rather than an improved global fit, a possibility that should be further tested with future high-precision observational data.