Quantum field theory of gravity with spin and scaling gauge invariance and spacetime dynamics with quantum inflation

Abstract

Treating the gravitational force on the same footing as the electroweak and strong forces, we present a quantum field theory of gravity based on spin and scaling gauge symmetries. A biframe spacetime is initiated to describe such a quantum gravity theory. The gravifield sided on both locally flat noncoordinate spacetime and globally flat Minkowski spacetime is an essential ingredient for gauging global spin and scaling symmetries. The locally flat gravifield spacetime spanned by the gravifield is associated with a noncommutative geometry characterized by a gauge-type field strength of the gravifield. A coordinate-independent and gauge-invariant action for the quantum gravity is built in the gravifield basis. In the coordinate basis, we derive equations of motion for all quantum fields including the gravitational effect and obtain basic conservation laws for all symmetries. The equation of motion for gravifield tensor is deduced in connection directly with the total energy-momentum tensor. When the spin and scaling gauge symmetries are broken down to a background structure that possesses the global Lorentz and scaling symmetries, we obtain exact solutions by solving equations of motion for the background fields in a unitary basis. The massless graviton and massive spinon result as physical quantum degrees of freedom. The resulting Lorentz-invariant and conformally flat background gravifield space-time is characterized by a cosmic vector with a nonzero cosmological mass scale. The conformal size of the Universe becomes singular at the cosmological horizon and turns out to be inflationary. A mechanism for quantum inflation is demonstrated to generate the inflation of the early Universe. Two types of gravity equation result, one is as the extension to Einstein's equation of general relativity, and the other is a new one that characterizes spinon dynamics.