Quantum cosmology with third quantisation

TL;DR

This paper reviews the canonical quantisation of spacetime geometry, focusing on third quantisation formalism for non-simply connected manifolds, and discusses universe creation, initial expansion, and matter emergence in quantum cosmology.

Contribution

It introduces and analyzes the third quantisation formalism for quantum cosmology, providing a framework for universe creation and evolution in non-simply connected manifolds.

Findings

Universe creation occurs in entangled universe-antiuniverse pairs.

Third quantisation formalism models the wave function as a quantum field.

Universes can emerge with initial expansion and matter after inflation.

Abstract

We review the canonical quantisation of the geometry of the spacetime in the cases of a simply and a non-simply connected manifold. In the former, we analyse the information contained in the solutions of the Wheeler-DeWitt equation and interpret them in terms of the customary boundary conditions that are typically imposed on the semiclassical wave functions. In particular, we review three different paradigms for the quantum creation of a homogeneous and isotropic universe. For the quantisation of a non-simply connected manifold the best framework is the so-called third quantisation formalism, in which the wave function of the universe is seen as a field that propagates in the space of Riemannian $3$-geometries, which turns out to be isomorphic to a (part of a) $1+5$ Minkowski spacetime. Thus, the quantisation of the wave function follows the customary formalism of a quantum field theory. A general review of the formalism is given and it is analysed the creation of the universes, their initial expansion and the appearance of matter after inflation. These features are presented in more detail in the case of a homogeneous and isotropic universe. The main conclusion in both cases is that the most natural way in which the universes should be created is in entangled universe-antiuniverse pairs.