On description of spatial topologies in quantum gravity

TL;DR

This paper proposes a novel approach to describe arbitrary spatial topologies in quantum gravity by generalizing third quantization near cosmological singularities, leading to modifications in quantum field theory.

Contribution

It introduces a new method for describing universe topologies through a generalized third quantization applicable near singularities.

Findings

The approach allows phenomenological modeling of arbitrary topologies.

It results in a modified quantum field theory framework.

Demonstrated with a free massless scalar field example.

Abstract

A new approach is suggested which allows to describe phenomenologically arbitrary topologies of the Universe. It consists in a generalizaton of third quantization. This quantization is carried out for the case of asymptotic closeness to a cosmological singularity. It is also pointed out that suggested approach leads to a modification of the ordinary quantum field theory. In order to show this modification we consider the example of a free massless scalar field.