Fuzzy Euclidean wormholes in anti–de Sitter space

Abstract

This paper is devoted to an investigation of Euclidean wormholes made by fuzzy instantons. We investigate the Euclidean path integral in anti-de Sitter space. In Einstein gravity, we introduce a scalar field with a potential. Because of the analyticity, there is a contribution of complexvalued instantons, so-called fuzzy instantons. If we have a massless scalar field, then we obtain Euclidean wormholes, where the probabilities become smaller and smaller as the size of the throat becomes larger and larger. If we introduce a non-trivial potential, then in order to obtain a nonzero tunneling rate, we need to tune the shape of the potential. With the O(4) symmetry, after the analytic continuation to the Lorentzian time, the wormhole throat should expand to infinity.However, by adding mass, one may obtain an instant wormhole that should eventually collapse to the event horizon. The existence of Euclidean wormholes is related to the stability or unitarity issues of anti-de Sitter space. We are not conclusive yet, but we carefully comment on these physical problems.

Suppression of long-wavelength CMB spectrum from the no-boundary initial condition

“…For example, we inves-tigated the quadratic potential for the inflaton [3] only, but it can be easily extended to the Starobinsky-type inflation models [4]. Also, we investigated for compact and homogeneous instantons, but there are other instantons that also explain the origin of our universe; e.g., the Coleman-De Luccia instantons [33] or the Euclidean wormholes [34][35][36][37]. One more brave question is this: what is the relation between the big bounce model of the loop quantum cosmology [17] and the Hartle-Hawking wave function [18]?…”

Fuzzy Instantons in Landscape and Swampland: Review of the Hartle–Hawking Wave Function and Several Applications

“…while the kinetic term has an opposite sign. Therefore, it is possible to determine a solution according to which the scalar field asymptotically approaches zero while there may exist a throat at the center [35]. One potential issue is whether the Euclidean action is well-defined or not.…”

“…The sufficient condition to obtain a finite action difference is that the field should approach zero sufficiently quickly near the infinity [36]. This can be achieved if we tune the shape of the potential [35].…”

Fuzzy Euclidean wormholes in the inflationary universe

“…This is, nevertheless, a special and restricted choice; indeed, it is more general to consider non-compact instantons which have two boundaries. The simplest example of this category is the Euclidean wormhole [13,15].…”

“…Rather, we will demonstrate that, so long as one imposes the restriction that the inflation must be lasted for more than 50 e-foldings, the wave function of the universe would prefer noncompact instantons over compact ones. The latter correspond to instantons proposed by Hartle and Hawking, while the former correspond to the so-called Euclidean wormholes [13][14][15]. This implies that our universe is more likely to have emerged from a Euclidean wormhole rather than a compact instanton, which in turn would give raise to several interesting implications.…”