Space for Both No-Boundary and Tunneling Quantum States of the Universe

TL;DR

This paper compares the Hartle-Hawking no-boundary and tunneling wavefunctions of the universe, showing that including a volume factor can reconcile the no-boundary proposal with observational data.

Contribution

It demonstrates that incorporating a volume factor into the probability distribution allows the no-boundary wavefunction to be consistent with observations at the minisuperspace level.

Findings

The no-boundary wavefunction peaks at small universes without volume correction.

Including a volume factor can make the no-boundary proposal compatible with observed universe sizes.

The tunneling wavefunction naturally favors larger universes, contrasting with the no-boundary case.

Abstract

At the minisuperspace level of homogeneous models, the bare probability for a classical universe has a huge peak at small universes for the Hartle-Hawking `no-boundary' wavefunction, in contrast to the suppression at small universes for the `tunneling' wavefunction. If the probability distribution is cut off at the Planck density (say), this suggests that the former quantum state is inconsistent with our observations. For inhomogeneous models in which stochastic inflation can occur, it is known that the idea of including a volume factor in the observational probability distribution can lead to arbitrarily large universes' being likely. Here this idea is shown to be sufficient to save the Hartle-Hawking proposal even at the minisuperspace level (for suitable inflaton potentials), by giving it enough space to be consistent with observations.