Neutrino Masses, the Gravitational Coupling Constant and the Cosmological Constant

We predict the masses of the three neutrino mass eigenstates to be m₁ = m₀, m₂ = 4 m₀ and m₃ = 22 m₀ where m₀ = 2.281 meV/c². We arrive at these predictions by applying two phenomenological postulates to neutrino oscillation data. First, we postulate that m₀ is the smallest quantum of mass and that the masses of all the massive elementary particles are positive integer multiples of m₀. Second, we postulate that the dark energy — which drives the accelerated expansion of the universe — is represented by a cosmological constant Λ, or, equivalently, a vacuum energy with constant density ρ_Λ = {α_g}⁴ ρ_P, where α_g = m₀/M_P is the gravitational coupling constant, M_P is the Planck mass and ρ_P is the Planck density. We also predict the squared–mass–difference ratio Δ₃₁/Δ₂₁ = ({m₃}² - {m₁}²)/({m₂}² - {m₁}²) to be exactly 32.2. We use neutrino oscillation data to predict the value of the cosmological constant Λ as well, in agreement with the νΛCDM model. In addition, we compute (i) the effective electron neutrino mass m_β, (ii) the upper bound on the effective Majorana mass of the electron neutrino m_{ββ} and (iii) the lower bounds on half-lives of various isotopes expected to undergo a neutrinoless double beta decay (0νββ). Finally, we introduce a new natural system of units in which both m₀ and ρ_Λ are set equal to unity.