Hartle-Hawking's vacuum is full of Vilenkin's universe-antiuniverse pairs

TL;DR

This paper explores the third quantisation formalism to show that the Hartle-Hawking vacuum contains universe-antiuniverse pairs, with the no boundary state equivalent to a thermal distribution of tunneling modes.

Contribution

It introduces a novel connection between Hartle-Hawking and Vilenkin boundary conditions through Bogolyubov transformations in third quantisation.

Findings

Hartle-Hawking vacuum is a thermal distribution of universe-antiuniverse pairs.

Modes related by Bogolyubov transformation connect different boundary conditions.

The no boundary state can be interpreted as a universe-antiuniverse pair ensemble.

Abstract

Within the third quantisation formalism, we find solutions of the Wheeler-DeWitt in terms of two sets of modes that can be identified with the Hartle-Hawking's no boundary condition and with the Vilenkin's tunneling boundary condition, respectively. The two sets of modes are related by a Bogolyubov transformation so the no boundary vacuum state turns out to be equivalent to a thermal distribution of tunnelling positive and negative modes representing, in a relative sense, universes and antiuniverses