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) =ma (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)/4G, 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). We make a connection between the cosmological constant of the Friedmann-Robertson-Walker model and the vacuum mass density of CGR by the relation I >=-8 pi G rho (vac) =3/tau (2). Each black hole particle defines its own volume of space enclosed by the event horizon, forming a sub-universe. 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 I mu (gamma) =(1-g)mc (2)/N (gamma) , where (1-g) is the fraction of the initial energy mc (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)mc(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. We give a model for ga parts per thousand Omega (b) (1+f)m (p) /m (n) , where m (n) is the neutron mass. Then ratio eta of the number of baryons N (b) to photons N (gamma) is given by eta = N-b/N-gamma approximate to alpha 2 Omega(b)fm(p)/m(n)/2(1 + f)[1 - Omega(b)(1 + f)m(p)/m(n)] (2) with a value of eta approximate to 6.708x10(-10). The Bekenstein-Hawking black hole entropy S is given by S=(kc (3) A)/(4A G), where k is Boltzmann's constant, A is Planck's constant over 2 pi and A is the area of the event horizon. For our black hole sub-universe of mass m the entropy is given by S = pi k tau(2)c(5)/(h) over barG, which can be put into the form relating to the vacuum mass density rho(vac) = rho(P)/(S/k), where the cosmological Planck mass density rho(P) = -M-P/L-P(3). The cosmological Planck mass M-P = root root 3/8 (h) over barc/G and length L-P = (h) over bar /M(P)c. The value of (S/k)approximate to 1.980x10(122).
International Journal Of Theoretical Physics