Exact recession velocity and cosmic redshift based on cosmological principle and Yang-Mills gravity

Based on the cosmological principle and quantum Yang-Mills gravity in the super-macroscopic limit, we obtain an exact recession velocity and cosmic redshift z, as measured in an inertial frame begin{document}$ Fequiv F(t,x,y,z). $end{document} For a matter-dominated universe, we have the effective cosmic metric tensor begin{document}$ G_{munu}(t) = (B^2(t),-A^2(t), -A^2(t),-A^2(t)),$end{document} begin{document}$ Apropto Bpropto t^{1/2} $end{document}, where begin{document}$ t $end{document} has the operational meaning of time in begin{document}$ F $end{document} frame. We assume a cosmic action begin{document}$ Sequiv S_{rm cos} $end{document} involving begin{document}$ G_{munu}(t) $end{document} and derive the ‘Okubo equation’ of motion, begin{document}$ G^{munu}(t)partial_mu S partial_nu S - m^2 = 0 $end{document}, for a distant galaxy with mass begin{document}$ m $end{document}. This cosmic equation predicts an exact recession velocity, begin{document}$ dot{r} = rH/[1/2 +sqrt{1/4+r^2H^2/C_o^2} ], where begin{document}$ H = dot{A}(t)/A(t) $end{document} and begin{document}$ C_o = B/A $end{document}, as observed in the inertial frame begin{document}$ F $end{document}. For small velocities, we have the usual Hubble's law begin{document}$ dot{r} approx rH $end{document} for recession velocities. Following the formulation of the accelerated Wu-Doppler effect, we investigate cosmic redshifts z as measured in begin{document}$ F $end{document}. It is natural to assume the massless Okubo equation, begin{document}$ G^{munu}(t)partial_mu psi_e partial_nu psi_e = 0 $end{document}, for light emitted from accelerated distant galaxies. Based on the principle of limiting continuation of physical laws, we obtain a transformation for covariant wave 4-vectors between and inertial and an accelerated frame, and predict a relationship for the exact recession velocity and cosmic redshift, begin{document}$ z = [(1+V_r)/(1-V_r^2)^{1/2}] - 1 $end{document}, where begin{document}$ V_r = dot{r}/C_o<1 $end{document}, as observed in the inertial frame begin{document}$ F $end{document}. These predictions of the cosmic model are consistent with experiments for small velocities and should be further tested.