Density perturbations in chain inflation

We consider the model of ‘chain inflation,’ in which the period of inflation in our universe took the form of a long sequence of quantum tunnelling events. We find that in the simplest such scenario, in which the tunnelling processes are uniform, approximately 104 vacua per e-folding of inflation are required in order for the density perturbations produced to be of an acceptable size. We arrive at this conclusion through a combination of analytic and numerical techniques, which could also serve as starting points for calculations with more general sets of assumptions.