A possible origin of the $\alpha$-vacuum as the initial state of the Universe

TL;DR

This paper explores the potential origin of the $ extalpha$-vacuum as an initial state of the universe, proposing that Euclidean wormholes can produce this vacuum, which generalizes the Bunch-Davies vacuum within a geometric framework.

Contribution

It demonstrates that Euclidean wormholes can give rise to the $ extalpha$-vacuum, providing a geometric origin and expanding understanding beyond the no-boundary scenario.

Findings

Euclidean wormholes allow for the $ extalpha$-vacuum state.

The Bunch-Davies vacuum is a special case of the $ extalpha$-vacuum.

Discussion of phase issues in the power spectrum for $ extalpha$-vacuum.

Abstract

We investigate the cosmological observables using the Euclidean path integral approach. Specifically, we study both the no-boundary compact instantons scenario and the Euclidean wormholes scenario that can induce the creation of two universes from nothing. It is known that perturbations associated with the no-boundary scenario can only be consistent with the Bunch-Davies vacuum. Here we demonstrate that the Euclidean wormholes can allow for a de Sitter invariant vacuum, the so-called $\alpha$-vacuum state, where the Bunch-Davies vacuum is a special case. This therefore provides the $\alpha$-vacuum a geometrical origin. As an aside, we discuss a subtle phase issue when considering the power spectrum related to $\alpha$-vacuum in the closed universe framework.