1005.4089 (Timothy D. Andersen)

An SO(4,1) group theory of quantum gravity    [PDF]

Timothy D. Andersen

The search for a quantum theory of gravity has become one of the most well-known problems in theoretical physics. Problems quantizing general relativity because it is not renormalizable have led to a search for a new theory of gravity that, while still agreeing with measured observations, is renormalizable. In this paper, I show that, given a "vortex" model of elementary particles in which rest mass derives from intrinsic spin and polarization, a Yang-Mills force with a SO(4,1) group symmetry predicts post-Newtonian N-body motion such as solar system observations of gravitational behavior as well as binary pulsar precession and orbital speed-up caused by gravitational radiation-reaction. I give a definition of the Yang-Mills theory on a lattice graph such that a background manifold is not required to define the theory. Using a homogeneous, isotropic universe model, I show that this theory does not contradict cosmological observations of Type 1a supernovae, Baryon Acoustic Oscillation, and the Cosmic Microwave Background. Most importantly, it agrees with the accelerating expansion of the universe as a consequence of the de Sitter group Lie algebra-an acceleration that I show does not occur in the Poincar\'e group approximation-suggesting that the de Sitter group symmetry explains dark energy. In addition, because it is a generic massless, semi-simple Yang-Mills theory, it is mathematically proved to be a perturbatively renormalizable quantum theory.

View original: http://arxiv.org/abs/1005.4089