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

Abstract

The Euclidean path integral is well approximated by instantons. If instantons are dynamical, they will necessarily be complexified. Fuzzy instantons can have multiple physical applications. In slow-roll inflation models, fuzzy instantons can explain the probability distribution of the initial conditions of the universe. Although the potential shape does not satisfy the slow-roll conditions due to the swampland criteria, the fuzzy instantons can still explain the origin of the universe. If we extend the Euclidean path integral beyond the Hartle–Hawking no-boundary proposal, it becomes possible to examine fuzzy Euclidean wormholes that have multiple physical applications in cosmology and black hole physics.

Novel Phenomena of the Hartle–Hawking Wave Function

“…It is worthwhile to compare with the classicality condition of the Euclidean path integral approach [14,15,19]. In our computations, we could not find any evidence to exclude initial conditions that violate the classicality condition.…”

“…About the latter point, i.e., a bias of η from exact 1, one may understand it by assuming that A is ϕ-dependent. In this case, A(ϕ)e −S E (ϕ) = e −S E (ϕ)+log A(ϕ) = e −S ′ (ϕ) , (19) and hence, the Euclidean action S E (ϕ) can be modified due to the ϕ-dependence of A. This might be a partial explanation for results beyond the Hawking-Moss instanton approximation.…”

Editorial to the Special Issue “Quantum Cosmology”

“…Recently, the 'landscape' feature from string and alike settings has been a frequent 'participant' in discussions. In [12], this is taken in a sincere appraisal concerning a specific (now iconic) solution for the universe in quantum cosmology. The fulcrum of 'time' was amply debated through [13,14].…”