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

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

arXiv comment6 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2110.05785

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