Exact recession velocity and cosmic redshift based on cosmological principle and Yang-Mills gravity * * Supported in part by Jing Shin Research Fund and Prof. Leung Memorial Fund of the UMassD Foundation

Abstract

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 For a matter-dominated universe, we have the effective cosmic metric tensor , where has the operational meaning of time in frame. We assume a cosmic action involving and derive the ‘Okubo equation’ of motion, , for a distant galaxy with mass . This cosmic equation predicts an exact recession velocity, , where and , as observed in the inertial frame . For small velocities, we have the usual Hubble's law for recession velocities. Following the formulation of the accelerated Wu-Doppler effect, we investigate cosmic redshifts z as measured in . It is natural to assume the massless Okubo equation, , 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, , where , as observed in the inertial frame . These predictions of the cosmic model are consistent with experiments for small velocities and should be further tested.