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Open Inflation Without False Vacua

S. W. Hawking, Neil Turok

Abstract

We show that within the framework of a definite proposal for the initial conditions for the universe, the Hartle-Hawking `no boundary' proposal, open inflation is generic and does not require any special properties of the inflaton potential. In the simplest inflationary models, the semiclassical approximation to the Euclidean path integral and a minimal anthropic condition lead to $Ω_0\approx 0.01$. This number may be increased in models with more fields or extra dimensions.

Open Inflation Without False Vacua

Abstract

We show that within the framework of a definite proposal for the initial conditions for the universe, the Hartle-Hawking `no boundary' proposal, open inflation is generic and does not require any special properties of the inflaton potential. In the simplest inflationary models, the semiclassical approximation to the Euclidean path integral and a minimal anthropic condition lead to . This number may be increased in models with more fields or extra dimensions.

Paper Structure

This paper contains 4 sections, 15 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Instantons
  3. The Value of $\Omega_0$
  4. Anthropic Estimate of $\Omega_0$

Figures (1)

  • Figure 1: Global structure of the open instanton and its continuation. The Euclidean region E is half of a deformed four sphere. It continues into a De Sitter like region II, and thence into an open inflating universe, region I. The dotted lines show the null surface (the 'bubble wall') emanating from the point $\sigma=0$ on the instanton. The heavy line shows the singularity discussed in the text.