Multi-field inflation with random potentials: field dimension, feature scale and non-Gaussianity

We explore the super-horizon evolution of the two-point and three-point correlation functions of the primordial density perturbation in randomly-generated multi-field potentials. We use the Transport method to evolve perturbations and give full evolutionary histories for observables. Identifying the separate universe assumption as being analogous to a geometrical description of light rays, we give an expression for the width of the bundle, thereby allowing us to monitor evolution towards the adiabatic limit, as well as providing a useful means of understanding the behaviour in $f_NL$. Finally, viewing our random potential as a toy model of inflation in the string landscape, we build distributions for observables by evolving trajectories for a large number of realisations of the potential and comment on the prospects for testing such models. We find the distributions for observables to be insensitive to the number of fields over the range 2 to 6, but that these distributions are highly sensitive to the scale of features in the potential. Most sensitive to the scale of features is the spectral index, with more than an order of magnitude increase in the dispersion of predictions over the range of feature scales investigated. Least sensitive was the non-Gaussianity parameter $f_NL$, which was consistently small; we found no examples of realisations whose non-Gaussianity is capable of being observed by any planned experiment.