Dynamic Models for the Beginning, Hubble Law and the Future of the Universe Based on Strong Cosmological Principle and Yang-Mills Gravity

We discuss highly simplified dynamic models for the beginning, expansion and future of the universe based on the strong cosmological principle and Yang-Mills gravity in flat space-time. We derive a relativistic Okubo equation of motion for galaxies with a time-dependent effective metric tensor $G_{\mu\nu}(t)$. The strong cosmological principle states that $G_{\mu\nu}(t)=\e_{\mu\nu} A^2(t)$ for $t \ge 0$. In a model (HHK) with Yang-Mills gravity in the super-macroscopic limit, one has $A(t)= a_o t^{1/2}$, which leads to the initial mass run away velocity $\dot{r}(0)=c$, associated with $r(0)=r_o>0$. Thus, the Okubo equation of motion for galaxies predicts a `detonation' at the beginning of the universe. The Okubo equation also implies $r(\infty) \to \infty$, $\dot{r}(\infty) \to 0$ with zero redshift for the future of the universe. In addition, the Okubo equation leads to the usual Hubble's law $\dot{r}(t) \approx H(t) r(t)$, where $H(t)=\dot{A}(t)/A(t)$ in non-relativistic approximation. We also discuss a model with a strict Hubble linear relation $\dot{r}(t) \approx const.\times r(t)$ for all time. This model gives a silent beginning of the universe: $\dot{r}(t)=0, \ \ddot{r}(t)\to\infty$ as $t \to 0$; and final radius $r(t) \to \infty,$ final velocity, $\dot{r}(t) \to c$, $\ddot{r}(t)\to 0$ as $t \to \infty$. In all models with the strong cosmological principle in flat space-time, Hubble's recession velocities are predicted to have a maximum, i.e., the speed of light, as measured in an inertial frame.