Constraints on the Sum of Neutrino Masses from ACT DR6 and DESI DR2 Considering Isocurvature Initial Conditions

We present a robust assessment of cosmological constraints on the sum of neutrino masses (sum m nu) when relaxing the standard assumption of purely adiabatic primordial initial conditions. Allowing for a neutrino density isocurvature (NDI) component alongside the adiabatic mode, we analyse the latest CMB-SPA combination (Planck 2018, ACT DR6, and SPT-3G), DESI DR2 baryon acoustic oscillation data, and the DES Year 5 supernova sample. Within the CDM model, the 95% upper limit weakens only marginally from sum m nu < 0.052 eV (purely adiabatic) to < 0.057 eV (including NDI), with the NDI amplitude consistent with zero. In the CPL dynamical dark energy model, the adiabatic limit is < 0.111 eV, shifting to < 0.115 eV with NDI, yet the isocurvature mode remains undetected. While these limits are robust against the inclusion of isocurvature perturbations, they are highly sensitive to both the assumed dark energy equation of state and the prior lower bound on sum m nu. Notably, the adiabatic CDM limit of 0.052 eV lies below the minimum sum required by the normal neutrino mass hierarchy (0.05878 eV), indicating that this bound is an artifact of the statistical prior extending to zero. Imposing a physically motivated hierarchy-informed prior raises the limit to < 0.092 eV. Our results demonstrate that current data show no evidence for NDI modes and that the inferred neutrino mass upper limit is robust against this extension, but a definitive, model-independent bound requires addressing prior dependencies and dark energy uncertainties. This work provides the first joint constraint on sum m nu and NDI using the full CMB-SPA+DESI DR2+DES dataset.