In defence of the `Tunneling' wave function of the Universe

TL;DR

This paper defends the tunneling wave function of the universe against recent criticisms, arguing it does not predict catastrophic black hole pair production in de Sitter space and clarifies its relation to the Hartle-Hawking wave function.

Contribution

It refutes claims that the tunneling wave function causes instabilities and clarifies its differences from the Hartle-Hawking wave function in cosmological models.

Findings

The tunneling wave function predicts a small, constant pair production rate.

Different horizon regions in de Sitter space cannot be treated as independent.

The tunneling wave function is not simply the inverse of the Hartle-Hawking wave function.

Abstract

The tunneling approach to the wave function of the universe has been recently criticized by Bousso and Hawking who claim that it predicts a catastrophic instability of de Sitter space with respect to pair production of black holes. We show that this claim is unfounded. First, we argue that different horizon size regions in de Sitter space cannot be treated as independently created, as they contend. And second, the WKB tunneling wave function is not simply the `inverse' of the Hartle-Hawking one, except in very special cases. Applied to the related problem of pair production of massive particles, we argue that the tunneling wave function leads to a small constant production rate, and not to a catastrophy as Bousso and Hawking's argument would suggest.