Volume Weighting in the No Boundary Proposal

Abstract

It has been suggested that the no boundary proposal would predict little or no slow roll inflation leading to an empty deSitter universe. However it is argued that the probability for the whole universe should be multiplied by a zero mode factor $e^{3N}$ which counts the number of Hubble volumes in the universe. This volume weighting is similar to that in eternal inflation but derived in a gauge invariant manner. It predicts that inflation began at a saddle point in the potential and that the universe was always in the semi-classical regime.