Space for both no-boundary and tunneling quantum states of the Universe

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” wave function, in contrast with the suppression at small universes for the “tunneling” wave function. 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.