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A model of multiverse in a three-dimensional quantum vacuum characterized by a variable energy density is proposed, where a relationship exists between the evolutionary possibilities of the generic universe and the corresponding fluctuations of the quantum vacuum energy density.A peculiar form of Wheeler-DeWitt equation, intended as an equation of background, in the picture of a "quantum Boltzmann statistics", is considered, which implies the generation of a cyclic multiverse where the evolutionary behaviour of each branch is fixed by the specific quantum vacuum energy density fluctuations characterizing that region of the landscape.A quantum field theory for the wave function of the multiverse in the curved minisuperspace formed by the scale factor and the scalar field that represents the energy-matter content of the universe, is developed.Finally, a suggestive interpretation of cosmological constant and dark matter is explored.
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