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Abstract:
In this thesis we investigate several phenomena in quantum gravity with a specific empha- sis on scale-invariant models of quadratic gravity whose actions contain all three independent squares of the Riemann tensor. After discussing the different ways in which scale invariance can manifest and reviewing how spontaneous symmetry breaking may occur as a result of quantum effects, we marry these concepts by constructing a model of gravity and matter that dynamically generates the Planck and electroweak scales through the spontaneous breaking of scale symme- try, thus describing an origin for the very concept of mass. We also demonstrate that this same scale-invariant model describes a period of cosmic inflation that is consistent with modern ob- servations. A simpler realization of this model with the same important features is then defined by including quantum effects that result from the traditionally neglected spin-2 ghost degrees of freedom that are inherently present in this type of theory. The second part of this work is devoted to studying the role of these spin-2 ghosts, which generically appear as negative norm states that threaten unitarity at the quantum level. We derive rigorous and novel covariant operator quanti- zations of both globally scale-invariant quadratic gravity in the phase of broken symmetry and of locally invariant conformal gravity in the unbroken phase. This leads us to establish the notion of “conditional unitary” wherein the broken phase theory is shown to be unitary up to very high energies, and grants a new perspective on the ghost problem in quantum gravity as a whole.
