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A cosmological model is proposed in which the Universe is created by quantum tunneling from "nothing" into a de Sitter space. The tunneling is described by a de Sitter---Hawking---Moss instanton. After the tunneling, the model evolves along the lines of the inflationary scenario. It is argued that at any time there exist parts of the Universe which are still in the de Sitter phase, while other parts have already recollapsed. This model does not have a big-bang singularity and does not require any initial or boundary conditions.
Alexander Vilenkin (Wed,) studied this question.