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A Yang-Mills Type Gauge Theory of Gravity and the Dark Matter Problem

Yi Yang, Wai Bong Yeung

Abstract

A Yang-Mills type gauge theory of gravity is shown to have a structure richer than that of Einstein's General Theory of Relativity. By elevating the full connections to independent dynamical gauge fields, the theory admits non-trivial vacuum configurations driven by gauge field self-interactions. We demonstrate that this non-linear geometric structure naturally yields an effective spacetime that explains the form of the galactic rotation curves and the anomalous amount of intergalactic gravitational lensing, completely circumventing the need for exotic dark matter particles.

A Yang-Mills Type Gauge Theory of Gravity and the Dark Matter Problem

Abstract

A Yang-Mills type gauge theory of gravity is shown to have a structure richer than that of Einstein's General Theory of Relativity. By elevating the full connections to independent dynamical gauge fields, the theory admits non-trivial vacuum configurations driven by gauge field self-interactions. We demonstrate that this non-linear geometric structure naturally yields an effective spacetime that explains the form of the galactic rotation curves and the anomalous amount of intergalactic gravitational lensing, completely circumventing the need for exotic dark matter particles.

Paper Structure

This paper contains 8 sections, 25 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. A Yang-Mills type gauge theory of gravity
  3. Two legitimate solutions
  4. Interpretation of the dual vacuum solutions in the Yang-Mills framework
  5. Predictions of the Universal rotation curves for spiral galaxies
  6. Right amounts of intergalactic gravitational lensing
  7. Conclusion
  8. Asymptotic Justification for Metric Superposition in the Weak-Field Limit

Figures (2)

  • Figure 1: The predicted relationship between the galactic rotation speed $v$ and the distance $r$ from a combined influence of the Newtonian force and the new geometric gauge field background: (a) The Milky Way, (b) NGC 3198, (c) NGC 2403 and (d) NGC 6503.
  • Figure 2: The orbital speeds of the planets in the solar system predicted with different effective gauge coupling weights $\alpha$. The geometric modifications are completely suppressed at this scale.