Studies on the quantum gravity effects in the early universe and black holes via string field theory and D-branes

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We investigated a three-dimensional gravitational theory on a noncommutative space which has a cosmological constant term only as a model which includes quantum gravity effects. We obtained various solutions that correspond to bubbles of spacetimes or interpolates zero metric and Minkowski metric and so on. All solutions we obtained are non-perturbative in the noncommutative parameter, therefore they are thought to be closely related to quantum gravity.We also investigated the fuzzy disc, which is a disc-shaped region in a noncommutative plane. We showed that one can introduce a concept of angles to the fuzzy disc, by using the phase operator and phase states known in quantum optics. As an application, we constructed fan-shaped soliton solutions of a scalar field theory on a fuzzy disc, which might correspond to a fan-shaped D-brane. We also applied this concept to an experimental test of noncommutativity by laser physics.