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

TL;DR

This paper develops simplified dynamic models of the universe's beginning, expansion, and future based on the strong cosmological principle and Yang-Mills gravity, predicting initial 'detonation' and asymptotic behaviors consistent with Hubble's law.

Contribution

It introduces novel flat-space-time models using Yang-Mills gravity and the strong cosmological principle, deriving equations that predict universe dynamics including initial explosion and future expansion.

Findings

Predicts a universe beginning with a 'detonation' at the speed of light.

Derives Hubble's law from the Okubo equation of motion.

Models suggest maximum recession velocity equals the speed of light.

Abstract

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.