Neutrino Masses, Gravitational Coupling Constant And Cosmological Constant

Masses of the three neutrino mass eigenstates are predicted to be m₀, 4m₀ & 22m₀ where m₀ = 2.281 meV/c². These predictions are arrived at by applying two ad-hoc postulates to neutrino oscillation data. First postulate is that the mass m₀ of the lightest neutrino mass eigenstate is the smallest quantum of mass and masses of all the massive elementary particles are positive integer multiples of m₀. The dimensionless gravitational coupling constant α_g is then defined as, α_g = m₀/M_p, where M_p is the Planck Mass. The second postulate is that the dark energy is represented by a cosmological constant Λ or, equivalently, a vacuum energy with constant density ρ_Λ = α_g⁴ ρ_p, where ρ_p is the Planck Density. These postulates also lead to the prediction of the value of (dimensionless) vacuum energy density to be Ω_Λ h² = 0.3344, in agreement with the ΛCDM model. Furthermore, the effective electron neutrino mass in β decay is predicted to be m_β = 4.02m₀. We also predict the effective Majorana mass of electron neutrino to be m_ββ ≤ 2.55m₀. This upper bound on m_ββ is then used to calculate lower bounds on half-lifes of various isotopes expected to undergo a neutrinoless double beta (0νββ) decay. Finally the two postulates are used to construct a natural system of units.