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

TL;DR

This paper explores third quantization in quantum cosmology within an extended minisuperspace framework, revealing fermionic universe creation and entanglement properties using Klein-Gordon and Dirac equations.

Contribution

It introduces a novel third quantization approach in an extended minisuperspace, analyzing universe creation and entanglement with both Klein-Gordon and Dirac formalisms.

Findings

Fermionic universe creation follows Fermi-Dirac statistics.

Entanglement entropy of multi-universe systems is computed.

Dirac-type wave functions provide new insights into universe number density.

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.