Quantum tunneling in the early universe

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Quantum tunneling in the early universe such as vacuum phase transition in the inflationary universe is deeply related to the large scale structure of the present universe. In this project, we systematically developed the method to analyze tunneling phenomena in the early universe, taking account of environments that are intrinsic to cosmology.In particular, in connection with the inflationary universe, we succeeded in obtaining the mode functions which describe the false vacuum in the de Sitter background. We then discovered that in order to correctly describe the quantum state inside a vacuum bubble, one must include a set of modes which are not normalizable in the usual sense (the so-called supercurvature modes on hyperbolic space). We have analyzed the effect of the bubble wall fluctuations which also give rise to supercurvature perturbations.Combining these results, we proposed a new inflationary model of the universe ; one-bubble open inflationary universe scenario. Taking account of the effect of the modes described above, as well as the usual continuous modes, on the quantum state inside a vacuum bubble, we investigated the predicted large angle anisotropies of the cosmic microwave background radiation due to these quantum fluctuations and gave constraints to theoretical models. We found our new scenario is a viable one that can successfully explain the large scale structure of the present universe.