A possible origin of the α-vacuum as the initial state of the Universe

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 α-vacuum state, where the Bunch-Davies vacuum is a special case. This therefore provides the α-vacuum a geometrical origin. As an aside, we discuss a subtle phase issue when considering the power spectrum related to α-vacuum in the closed universe framework.