The No-Boundary Wave Function and the Duration of the Inflationary Period

TL;DR

This paper derives analytic expressions for the boundary between Euclidean and Minkowskian regions in a simple cosmological model, predicting the initial scalar field value for inflation, and explores models compatible with a sufficiently long inflationary period.

Contribution

It provides the first analytic expressions for the caustic and breakdown value in the no-boundary wave function framework, linking initial conditions to inflation duration.

Findings

Derived analytic expressions for the caustic and breakdown value.

Identified inflationary models compatible with the no-boundary proposal.

Predicted initial scalar field values for sufficient inflation.

Abstract

For the simplest minisuperspace model based on a homogeneous, isotropic metric and a minimally coupled scalar field we derive analytic expressions for the caustic which separates Euklidean and Minkowskian region and its breakdown value $\p_*$. This value represents the prediction of the no-boundary wave function for the scalar field at the beginning of inflation. We use our results to search for inflationary models which can render the no-boundary wave function consistent with the requirement of a sufficiently long inflationary period.