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

• Published in: arXiv.org 2021-04
• Main Authors: Jong-Ping Hsu, Hsu, Leonardo
• Format: Article
• Language: English
• Subjects: Astronomical models; Detonation; Dynamic models; Equations of motion; Galaxies; Light speed; Red shift; Relativistic effects; Relativity; Spacetime; Tensors; Time dependence; Universe
• ISSN: 2331-8422

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.