Fuzzy Euclidean wormholes in the inflationary universe

Abstract

In this paper, we investigate complex-valued Euclidean wormholes in the Starobinsky inflation.Due to the properties of the concave inflaton potential, the classicality condition at both ends of the wormhole can be satisfied, as long as the initial condition of the inflaton field is such that it is located sufficiently close to the hilltop. We compare the probabilities of classicalized wormholes with the Hartle-Hawking compact instantons and conclude that the Euclidean wormholes are probabilistically preferred than compact instantons, if the inflation lasts more than 50 e-foldings. Our result assumes that the Euclidean path integral is the correct effective description of quantum gravity. This opens a new window for various future investigations that can be either confirmed or refuted by future experiments. *

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

“…where , A, and α are free parameters (see Figure 7 [27]). This model provides a flat hilltop [28] that is consistent with the Starobinsky model [29], which is preferred by the recent Planck data analysis [30]. In this model, the scalar field at the end of the wormhole rolls down to the local minimum, and hence the primordial inflation is naturally terminated.…”

“…Re φ e −2ωt → 0, (28) and hence after the Wick-rotation, the solution will eventually satisfy the classicality conditions. On the other hand, if µ > 3/2, the solutions satisfy under-damped motion.…”

“…The largest probability of compact instantons occurs close to the cutoff, where it is generally larger than that of the Euclidean wormholes that appear only near the hilltop. On the other hand, if we assume a mechanism that enhances the large e-foldings (e.g., introducing a massive field direction), Euclidean wormholes will be more highly favored than compact instantons [28]. Therefore, as long as we assume that our universe experienced more than 50 e-foldings, a Euclidean wormhole with a concave potential will be preferred over compact instantons with convex or concave potentials.…”