Third quantization for scalar and spinor wave functions of the Universe in an extended minisuperspace

Abstract

Abstract We consider the third quantization in quantum cosmology of a minisuperspace extended by the Eisenhart–Duval lift. We study the third quantization based on both Klein–Gordon type and Dirac-type equations in the extended minisuperspace. Spontaneous creation of ‘Universes’ is investigated upon the quantization of a simple model. We find that the quantization of the Dirac-type wave function reveals that the number density of universes is expressed by the Fermi–Dirac distribution. We also calculate the entanglement entropy of the multi-universe system.