Weighing neutrinos in Finslerian cosmological models

To explore the neutrino physics in the framework of Finsler geometry, we perform constraints on five cosmological models using the most stringent constraint we can provide so far. For the first time, we give the 95% limits of the total mass of three active neutrinos Sigma m(nu) for three Finslerian models in the presence of massive neutrinos. We find that the base Finslerian model, a two-parameter extension to the ACDM model based on the Finsler geometry, can fit better to current data than the other four models, and that the values of constrained effective typical parameters alpha and ss in four Finslerian models are all consistent with zero at the 1 sigma confidence level (CL), indicating that four Finslerian models just deviate very slightly from the ACDM model. For the base Finslerian model with a constant equation of state (EoS) of dark energy (DE) and massive neutrinos, we obtain a tighter constraint on the EoS of DE, which is more stringent than Planck's prediction by one order of magnitude. For the nonflat base Finslerian model with massive neutrinos, we find that our measured value of spatial curvature is in a strong tension with a flat universe at the 2.45 sigma CL. However, if fixing Sigma m(nu) = 0.06 eV with a normal hierarchy, this tension vanishes, i.e., a flat universe is still preferred in the nonflat base Finslerian model. We also find that the current H-0 tension can be effectively alleviated by four Finslerian models.