Unification of Gravitation, Gauge Field and Dark Energy

TL;DR

This paper proposes a unification of gravitation with gauge fields through the concept of a complex daor field, explaining dark energy as a consequence of space-time curvature self-coupling, consistent with observations.

Contribution

It introduces the daor field and its geometry, unifies gravity with gauge fields via complex connections, and links dark energy to curvature self-coupling.

Findings

Dark energy density matches astronomical observations

Einstein's equations emerge from the daor field framework

G and gauge coupling constants are related by G=λ²ε²

Abstract

This paper is composed of two correlated topics: 1. unification of gravitation with gauge fields; 2. the coupling between the daor field and other fields and the origin of dark energy. After introducing the concept of ``daor field" and discussing the daor geometry, we indicate that the complex daor field has two kinds of symmetry transformations. Hence the gravitation and SU(1,3) gauge field are unified under the framework of the complex connection. We propose a first-order nonlinear coupling equation of the daor field, which includes the coupling between the daor field and SU(1,3) gauge field and the coupling between the daor field and the curvature, and from which Einstein's gravitational equation can be deduced. The cosmological observations imply that dark energy cannot be zero, and which will dominate the doom of our Universe. The real part of the daor field self-coupling equation can be regarded as Einstein's equation endowed with the cosmological constant. It shows that dark energy originates from the self-coupling of the space-time curvature, and the energy-momentum tensor is proportional to the square of coupling constant \lambda. The dark energy density given by our scenario is in agreement with astronomical observations. Furthermore, the Newtonian gravitational constant G and the coupling constant \epsilon of gauge field satisfy G= \lambda^{2}\epsilon^{2}.