Gravitational Coupling Constant, Neutrinos And Cosmological Constant

Masses of the three neutrino mass eigenstates are predicted to be m₀, 4m₀ & 22m₀ where m₀ = 2.283 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 integral 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 = α⁴_g ρ_p, where ρ_p is the Planck Density. These postulates are then used to predict the value of vacuum energy density to be Ω_Λ h² = 0.3354 which is in agreement with the ΛCDM model. Furthermore, the effective neutrino mass of the β decay is predicted to be m_β = 4.02m₀. We also predict the effective Majorana mass of the neutrinoless double beta decay (0νββ) to be m_ββ ≤ 2.55m₀. This upper bound on m_ββ is then used to calculate the lower bounds on the half-lifes of various isotopes expected to undergo 0νββ. Finally the two postulates are used to construct a natural system of units