NUTs, Bolts and Stokes Phenomena in the No-Boundary Wave Function

TL;DR

This paper analyzes the no-boundary wave function in a biaxial Bianchi IX universe with a positive cosmological constant, revealing Stokes phenomena that influence saddle point dominance and phase transitions.

Contribution

It extends the analysis of the no-boundary wave function by identifying Stokes phenomena affecting saddle points in a biaxial Bianchi IX model with positive cosmological constant.

Findings

Two Stokes phenomena occur at large squashing parameters.

Stokes phenomena eliminate certain saddle point geometries.

Phase transitions occur where NUT and Bolt saddle points exchange dominance.

Abstract

In this note, we revisit and extend the analysis of the no-boundary wave function for the minisuperspace model in which the universe is described by a biaxial Bianchi IX metric. As matter content, we simply assume a positive cosmological constant. We find that two Stokes phenomena occur, at large squashing parameters of the spatial section of the universe. These Stokes phenomena eliminate potentially dominant Taub-Bolt-de Sitter saddle point geometries and are crucial for the consistency of the model. They also imply that phase transitions occur at certain levels of squashing, where NUT and Bolt saddle points exchange dominance.