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.
Highlights
PreliminariesIn modern physics, understanding the nature of the origin of the universe is one of the most fundamental problems
Where τ is the Euclidean time, dΩ23 is the 3-sphere, and a(τ) is the scale factor. In addition to this symmetry, if we impose the on-shell condition to the metric and matter field; or we restrict to instantons, we can approximate the wave function based on the steepest-descent approximation: Ψ[b, ψ]
Fuzzy Instantons with Slow-Roll Inflation The first issue is to obtain classicalized fuzzy instantons based on slow-roll inflation
Summary
In modern physics, understanding the nature of the origin of the universe is one of the most fundamental problems. Due to the singularity theorem [1], if we move backward in time and assume reasonable physical conditions, it appears that there must exist an initial singularity. At this singularity, all the laws of general relativity break down; a quantum gravitational prescription is required. The most conservative approach is to quantize the gravitational degrees of freedom as per the canonical quantization method [2] Using this approach, one can obtain the quantized Hamiltonian constraint; or the so-called Wheeler–DeWitt equation. By selecting a certain boundary condition, one may or may not provide a reasonable probability distribution for the early universe. There is no fundamental principle that can be used to select the boundary condition; in principle, the boundary condition must be confirmed by the possible observational consequences [4]
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