Quantum Creation of an Open Inflationary Universe

TL;DR

This paper compares the Hartle-Hawking and tunneling wave functions in quantum cosmology, arguing that the tunneling wave function better predicts a universe with Omega close to 1, aligning with inflationary expectations.

Contribution

It clarifies the applicability of different wave functions in quantum creation of the universe and emphasizes the tunneling wave function's consistency with inflationary flatness.

Findings

Hartle-Hawking wave function predicts Omega ≈ 0.01, inconsistent with observations.

Tunneling wave function predicts Omega ≈ 1, matching inflationary models.

Certain models allow Omega to vary widely, from greater than 1 to much less than 1.

Abstract

We discuss a dramatic difference between the description of the quantum creation of an open universe using the Hartle-Hawking wave function and the tunneling wave function. Recently Hawking and Turok have found that the Hartle-Hawking wave function leads to a universe with Omega = 0.01, which is much smaller that the observed value of Omega > 0.3. Galaxies in such a universe would be about $10^{10^8}$ light years away from each other, so the universe would be practically structureless. We will argue that the Hartle-Hawking wave function does not describe the probability of the universe creation. If one uses the tunneling wave function for the description of creation of the universe, then in most inflationary models the universe should have Omega = 1, which agrees with the standard expectation that inflation makes the universe flat. The same result can be obtained in the theory of a self-reproducing inflationary universe, independently of the issue of initial conditions. However, there exist two classes of models where Omega may take any value, from Omega > 1 to Omega << 1.