Quantum aspects of different formulations of general relativity

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The theory of general relativity which describes our current best understanding of gravity can be defined in terms of different variables and different classical actions. While these different formulations agree in their classical solutions and predictions, it is much less clear whether they have the same quantum behaviour. For example replacing the metric by a (self-dual) spin connection as a fundamental variable can lead to the construction of loop quantum gravity, a theory that does not exist in the original metric formulation. This project will study various formulations of general relativity, in particular those in which the spin connection plays a fundamental role, and compare their quantum properties. A focus will be on symmetric cosmological models where quantisation can be achieved unambiguously and without the pathologies of standard quantum gravity.