Euclidean quantum gravity and stochastic approach: Physical reality of complex-valued instantons

TL;DR

This paper explores the connection between Euclidean quantum gravity and stochastic inflation, demonstrating that complex-valued instantons correspond to certain probability distributions and interpreting Euclidean manifolds as coarse-graining scales.

Contribution

It establishes a deeper relation between stochastic inflation and Euclidean quantum gravity by linking complex instantons to probability distributions beyond static potentials.

Findings

Complex-valued instantons correspond to non-zero probability field values.

Euclidean manifolds can be viewed as coarse-graining scales.

The approach extends the connection between stochastic and Euclidean frameworks.

Abstract

In this talk, we compare two states: the stationary state in stochastic inflation and the ground state wave function of the universe. We already know that, for the potential with a static field, two pictures give the same probability distribution. Here, we go beyond this limit and assert that two pictures indeed have deeper relations. We illustrate a simple example so that there is a corresponding instanton if a certain field value has a non-zero probability in the statistical side. This instanton should be complex-valued. Furthermore, the compact manifold in the Euclidean side can be interpreted as a coarse-graining grid size in the stochastic universe. Finally, we summarize the recent status and possible applications.