Classical and Quantum Surgery of Geometries in an Open Inflationary Universe

TL;DR

This paper investigates classical and quantum Euclidean geometries compatible with open inflationary universes, revealing conditions for geometry matching at singularities and deriving wave functions for quantum universe creation.

Contribution

It introduces a detailed analysis of Euclidean geometries in open inflation, including the effects of matter states and instanton regularity, and derives wave functions for quantum creation.

Findings

Matching conditions depend on matter state (ordinary or exotic).

Exotic matter allows for regular instantons at finite boundaries.

Wave functions describe quantum creation of open inflationary universes.

Abstract

We study classically and quantum mechanically the Euclidean geometries compatible with an open inflationary universe of a Lorentzian geometry. The Lorentzian geometry of the open universe with an ordinary matter state matches either an open or a closed Euclidean geometry at the cosmological singularity. With an exotic matter state it matches only the open Euclidean geometry and describes a genuine instanton regular at the boundary of a finite radius. The wave functions are found that describe the quantum creation of the open inflationary universe.