Gauge Theories of Conformal Gravitation

In this thesis we investigate the locally scale-invariant theories of conformal and Weyl quadratic gravity, and the ensuing relationship between them. Using a Yang-Mills inspired gauge theory perspective, we derive the actions describing these theories and discuss their phenomenologies. Particular focus is put on the physically propagating degrees of freedom in each theory, as well as the cosmological implications of conformal gravity and the dimensional transmutation that occurs naturally in Weyl quadratic gravity. The issue of Ostrogradsky instabilities that arise from the fourth-order derivatives present in both theories is also discussed. Finally, using a process known as Ricci gauging, we find that conformal gravity can be viewed as gauged-fixed Weyl quadratic gravity, and we speculate on the existence of an alternative gauge fixing procedure that leads to a new theory which is dual to conformal gravity