Neutrino mass constraints in interacting dark energy models after DESI DR2

Recent DESI observations indicate a deviation from the $\Lambda$CDM model, showing a preference for dynamical dark energy and thereby relaxing the upper limit on the neutrino mass within this framework. This deviation can also be explained by the presence of an interaction between dark energy and dark matter. In this work, we investigate the cosmological upper bounds on the total neutrino mass ($\sum m_{\nu}$) across four different interacting dark energy (IDE) models. The present analysis employs the latest DESI baryon acoustic oscillation, cosmic microwave background, and type Ia supernova datasets. These results demonstrate that the upper bounds on $\sum m_{\nu}$ exhibit profound sensitivity to the specific phenomenological formulation of the interaction term. While the I$\Lambda$CDM2 model ($Q \propto H \rho_{\mathrm{c}}$) substantially relaxes the stringent upper limit ($\sum m_{\nu} < 0.129$ eV at 95% confidence level), notably the I$\Lambda$CDM3 model ($Q \propto H_0 \rho_{\mathrm{de}}$), severely compresses the allowed parameter space, yielding a highly restrictive bound of $\sum m_{\nu} < 0.051$ eV. Furthermore, rigorous goodness-of-fit evaluations utilizing the Deviance Information Criterion and $\Delta\chi^2_{\mathrm{MAP}}$ indicate that the current observational data statistically favor these mass-suppressing IDE models. This establishes an exacerbated statistical tension between the observationally preferred IDE scenarios and the normal hierarchy lower bound ($\sim 0.06$ eV) determined by terrestrial neutrino oscillation experiments.