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 F≡F(t,x,y,z). For a matter-dominated universe, we have the effective cosmic metric tensor Gμν(t)=(B^2(t),-A^2(t),-A^2(t),-A^2(t)), A∝B∝t^1/2, where t has the operational meaning of time in F frame. We assume a cosmic action S≡Scos involving Gμν(t) and derive the ‘Okubo equation’ of motion, G^μν(t)■μS■νS-m^2=0, for a distant galaxy with mass m. This cosmic equation predicts an exact recession velocity, r=rH/[1/2+√1/4+r^2H^2/C0^2]<Co, where H=A(t)/A(t) and Co=B/A, as observed in the inertial frame F. For small velocities, we have the usual Hubble's law r≈rH for recession velocities. Following the formulation of the accelerated Wu-Doppler effect, we investigate cosmic redshifts z as measured in F. It is natural to assume the massless Okubo equation, G^μν(t)■μψe■νψe=0, 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, z=[(1+Vr)/(1-Vr^2)1/2]-1, where Vr=r/Co<1, as observed in the inertial frame F. These predictions of the cosmic model are consistent with experiments for small velocities and should be further tested.