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

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 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,ṙ = rH/[1/2 + 1/4 + r 2 H 2 /C 2 o ] < Co, where H =Ȧ(t)/A(t) and Co = B/A, as observed in the inertial frame F . For small velocities, we have the usual Hubble's lawṙ ≈ 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−V 2 r ) 1/2 ]−1, where Vr =ṙ/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.

Dark Matter, Cosmic Positrons in Alpha Magnetic Spectrometer Experiment and Particle-Cosmology with Yang-Mills Gravity

“…The combination of gauge symmetry and an effective metric tensor provides a framework for and leads to alternative dynamics of cosmic expansion based on Yang-Mills gravity at the super-macroscopic limit. In this super-macroscopic limit with the cosmological principle, one has cosmic Okubo equation for the motion of distant galaxies and for cosmic red shifts, which are consistent with experiments [7].…”

“…CPT invariance implies a maximum symmetry between particle and antiparticle, e.g., lifetime and mass equalities between particles and antiparticles [2]. According to the Big Jets model, [7] one may picture two jets as two gigantic fireballs expanding and moving away in opposite directions in the beginning of the universe. Each jet has extremely large number of quarks and antiquarks.…”

“…The evolution in each fireball after the neutron (or anti-neutron) decay is similar to that in a hot big bang. Thus, the Big Jets model with CPT invariance [7] predicts that the antimatter half-universe has electron-neutrinos 'anti-dark-matter' and should be far away from our matter half-universe. Hence, we cannot detect antimatter in our matter half-universe.…”

“…To understand the anti-e-neutrino dark matter, let us briefly discuss the framework of particle-cosmology [7]. Particle physics and quantum field theories are closely related to the Poincaré transformations (or the Poincaré group) in flat space-time.…”

“…Let us now make the discussion quantitative and include both leptonic and (Yang-Mills) gravitational interactions in the Lagrangian L ℓφ [7,8] within the framework of particle-cosmology. In an inertial frame, the Lagrangian L ℓφ involving a set of leptons ℓ = (e, ν e ), the leptonic U 1 gauge field L µ (x), and gravitational spin-2 fields[4] φ µν (x) takes the form,…”