基于宇宙学原理和Yang-Mills引力的精确后退速度和宇宙红移
Exact Recession Velocity and Cosmic Redshift Based on Cosmological Principle and Yang-Mills Gravity
摘要：
基于宇宙学原理和超宏观极限下的量子Yang-Mills引力，我们得到了在惯性系$F\equiv F(t,x,y,z).$中测量的精确的后退速度和宇宙红移z。对于物质支配的宇宙，我们得到了有效的宇宙度规张量$G_{μν}(t)=(B^2(t),-A^2(t),-A^2(t),-A^2(t)), \ A\propto B\propto t^{1/2}$，其中$t$在$F\equiv F(t,x,y,z).$系中具有时间的运算意义。我们假设宇宙的行动$S\equiv S_{cos}$涉及$G_{μν}(t)$和推导出'大久保运动方程，$G^{μν}(t)\partial_μS \partial_νS - m^2=0$，为一个遥远的星系与质量$m$。这个宇宙方程预言了一个精确的后退速度，$\dot{r}=rH/[1/2 +\sqrt{1/4+r^2H^2/C_o^2} ]<C_o$，其中$H=\dot{A}(t)/A(t)$和$C_o=B/A$，如在惯性系$F$中观察到的。对于较小的速度，我们有通常的哈勃定律$\dot{r} \approx rH$的衰退速度。根据加速吴-多普勒效应的公式，我们研究了在$F$中测量的宇宙红移z.对于从加速的遥远星系发出的光，我们很自然地假设大久保方程（$G^{μν}(t)\partial_μψ_e \partial_νψ_e=0$）是无质量的。根据物理定律的极限延拓原理，得到了协变波矢在惯性系和加速系之间的变换，并预言了在惯性系$F$中观测到的精确后退速度与宇宙红移的关系式$z=[(1+V_r)/(1-V_r^2)^{1/2}] - 1$，其中$V_r=\dot{r}/C_o<1$.宇宙模型的这些预测与小速度的实验是一致的，应该进一步检验。
英文摘要：
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 $F\equiv F(t,x,y,z).$ For a matter-dominated universe, we have the effective cosmic metric tensor $G_{μν}(t)=(B^2(t),-A^2(t),-A^2(t),-A^2(t)), \ A\propto B\propto t^{1/2}$, where $t$ has the operational meaning of time in $F$ frame. We assume a cosmic action $S\equiv S_{cos}$ involving $G_{μν}(t)$ and derive the `Okubo equation' of motion, $G^{μν}(t)\partial_μS \partial_νS - m^2=0$, for a distant galaxy with mass $m$. This cosmic equation predicts an exact recession velocity, $\dot{r}=rH/[1/2 +\sqrt{1/4+r^2H^2/C_o^2} ]<C_o$, where $H=\dot{A}(t)/A(t)$ and $C_o=B/A$, as observed in the inertial frame $F$. For small velocities, we have the usual Hubble's law $\dot{r} \approx rH$ 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, $G^{μν}(t)\partial_μψ_e \partial_νψ_e=0$, 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, $z=[(1+V_r)/(1-V_r^2)^{1/2}] - 1$, where $V_r=\dot{r}/C_o<1$, 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.
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