Abstract. 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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