Comparison between gauge theory gravity and general relativity

Abstract

A new theory of gravitation (Gauge Theory Gravity) was recently developed. This is constructed in fiat background spacetime and uses gauge fields to ensure that all relations between physical quantities are variant with respect to position and orientation of the matter fields. The theory starts from a different set of axioms but it is locally equivalent to General Relativity if spin effects are ignored. In this work I develop the linearized theory of gravity, including gravitational waves, using Gauge Theory Gravity. I also review the theory, examining its physical consequences and discussing its validity as a theory of gravitation. Starting with a review of the development of theories of gravity leading up to Gauge Theory Gravity, including alternative theories to General Relativity, I discuss the requirements for a valid physical theory. The fundamental concepts of gauge theory are also discussed. Gauge theory gravity is then presented, starting with an exposition of the formalism of geometric algebra, with a derivation of the field equations. The concept of a gauge theory is then discussed using electromagnetism as an example, in both its Classical and Quantum formulation. The fundamental differences between the gauge theories for gravitation and electromagnetism are studied. A derivation of the linearized theory of gravity based on gauge principles is then presented, comparing the geometric algebra and tensor formalisms. The results obtained for gravitational waves are found to agree with the General Relativistic derivation. Finally, I investigate the extent to which we can distinguish between General Relativity and Gauge Theory Gravity, and discuss the physical and cosmological parameters which could be used for such a purpose.