Utilizing a dimensional analysis, Vavel found a formula for the neutrino mass depending on the Hubble constant H, yielding a mass value of 4.26 meV. Recently, a related formula for the electron neutrino was proposed by Mongan, depending on H and the dark energy parameter Ω_Λ. He assumed a spherical model for the electron neutrino and he proposed that its mass depends on the low mass density of the Universe. Furthermore, he assumed that its mass is constrained by the Compton wavelength. The obtained formula predicts a mass m₁ of 1.37 meV.

An alternative formula for the mass m₁ of the electron neutrino, also depending on H and Ω_Λ, can be obtained from a toroidal model of leptons, recently proposed by Biemond. In this model a toroidal shape is assumed for the electron neutrino with a radius r₁ of the torus and a radius r₂ of the tube. This torus is assumed to be filled with the low mass density of the Universe. A mass m₁ of 1.52 meV is obtained in this case.

By combination of the magnetic moment of a massive Dirac neutrino, deduced in the context of electroweak interactions at the one-loop level, and a magnetic moment for a neutrino arising from gravitational origin, a formula for the neutrino mass m₁ was obtained in 2015. This result depending on the Fermi constant forms a bridge between electroweak interactions and gravitation. In this case a more accurate value of 1.530 meV was obtained for mass m₁.