| In this work, we analyze two different aspects of the formulation of Quantum Gravity using the Wave Function of the Universe approach.; In Part I we search for a way to define nonperturbatively the wave function, in the context of gravity in 2+1 dimensions, making use of the conjectured duality between the latter and 2-d conformal field theory on the spacetime boundary. In the pure gravity case, it has been known that the Wheeler-DeWitt equation, that formally defines the wave function, can be interpreted as a Ward identity for the boundary theory, which in this case can be identified with a model with affine sl(2, R) invariance. We try to extend this method to the general case when gravity is coupled to matter. What makes this possible is our finding that there exist a boundary affine sl(2, R) algebra structure also in the most general case: any two dimensional conformal field theory can be universally embedded into a larger structure that carries an action for that algebra.; Part II has a more phenomenological nature. Here, the wave function of the universe is defined in a cosmological setting, where it describes the quantum metric fluctuations on a fixed classical background. In this context it is actually possible to give a well-defined meaning to the wave function of the universe, which is directly related to the spectrum of anisotropies in the Cosmic Microwave Background radiation. Due to the high precision of future probes, It might be possible to observe effects of high energy physics on the spectrum of these anisotropies.; To study these effects, we use the recently developed technique of boundary effective field theory. In this framework, we the effects of non-Gaussianities in the initial state in inflationary cosmology, and we consider the problem of naturalness and fine-tuning of the boundary theory, asking whether it is possible for it to be natural and at the same time potentially observable.; We apply these methods to recently proposed cyclic cosmological models, finding that, generically, they are in conflict with observation, and they need fine-tuning to be considered viable. |
