Particle Pair Production in Cosmological General Relativity
  The Cosmological General Relativity (CGR) of Carmeli, a 5-dimensional (5-D) theory of time, space and velocity, predicts the existence of an acceleration a_0 = c / tau due to the expansion of the universe, where c is the speed of light in vacuum, tau = 1 / h is the Hubble-Carmeli time constant, where h is the Hubble constant at zero distance and no gravity.   The Carmeli force on a particle of mass m is F_c = m a_0, a fifth force in nature.   In CGR, the effective mass density rho_eff = rho - rho_c, where rho is the matter density and rho_c is the critical mass density which we identify with the vacuum mass density rho_vac = -rho_c.   The fields resulting from the weak field solution of the Einstein field equations in 5-D CGR and the Carmeli force are used to hypothesize the production of a pair of particles.   The mass of each particle is found to be m = tau c^3 / 4 G, where G is Newton's constant.   The vacuum mass density derived from the physics is rho_vac = -rho_c = -3 / (8 pi G tau^2).   The cosmic microwave background (CMB) black body radiation at the temperature T_o = 2.72548 K which fills that volume is found to have a relationship to the ionization energy of the Hydrogen atom. Define the radiation energy epsilon_gamma = (1 - g) m c^2 / N_gamma, where (1-g) is the fraction of the initial energy m c^2 which converts to photons, g is a function of the baryon density parameter Omega_b and N_gamma is the total number of photons in the CMB radiation field. We make the connection with the ionization energy of the first quantum level of the Hydrogen atom by the hypothesis epsilon_gamma = [(1 - g) m c^2] / N_gamma = alpha^2 mu c^2 / 2, where alpha is the fine-structure constant and mu = m_p f / (1 + f), where f= m_e / m_p with m_e the electron mass and m_p the proton mass. 
Firmin J. Oliveira
physics.gen-ph