Physics – General Physics
Scientific paper
2012-03-21
Physics
General Physics
14 pages, 0 figures
Scientific paper
The Cosmological General Relativity of Carmeli, a 5-dimensional 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. The fields resulting from the solution of the Einstein field equations in 5-D CGR and the Carmeli force are used to hypothesize the production of a particle and its antiparticle. 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 $\rho_{vac} = -3/8 \pi G \tau^2$. The cosmological constant is then given by $\Lambda = 3 / \tau^2$. We derive an expression for $\tau$ given by $\tau = \sqrt{(45 \zeta (1 - g) c^3 \hbar^3) / (4\pi^3 G \mu \alpha^2 k^3 \beta^3 T^3)}$, where $\zeta$ is the blackbody mean energy coefficient, $(1 - g)$ is the fraction of the original mass $m$ which resulted in matter-antimater annihilations during the big-bang, $\hbar$ is Planck's constant over $2 \pi$,$\mu = m_e m_p / (m_e + m_p)$, with $m_e$ the electron mass and $m_p$ the proton mass, $\alpha$ is the fine-structure constant, $k$ is Boltzmann's constant, $\beta= (1 + z)^{-1}$ where z is the cosmological redshift and $T$ is the CMB temperature. For $g = 0.04$ and $\beta=1$ at the present epoch we obtain the values for $\tau \approx 4.153 \times 10^{17} {\rm s}$ and $h = 1 / \tau \approx 74.31 {\rm km} {\rm s}^{-1} {\rm Mpc}^{-1}$. For $f = m_e/m_p$ the ratio of nucleons $N_n$ to photons $N_{\gamma}$ is given by $N_n / N_{\gamma} = (\alpha^2 g f) / (2 (1 - g) (1 + f)^2)$, with a value of $N_n / N_{\gamma} \approx 6.04 \times 10^{-10}$.
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