Non-Uniqueness of Classical Inflationary Trajectories on a High-Dimensional Landscape

Motivated by the string landscape, inflation may happen on a high dimensional complicated potential. We propose a new way to construct some high dimensional random potentials, and study inflation on top of that, for up to 50-dimensions in field space. Especially, random bifurcations of classical inflationary trajectory are studied. It is shown that the bifurcation probability increases as a function of number of dimensions. Those random bifurcations are not consistent with observations, and dramatically limit the parameter space of inflation on a complicated landscape. For example, in 10 dimensions, only $10^{-3} \sim 10^{-6}$ of the parameter space volume leads to unique classical trajectories. The rest is ruled out by random bifurcations.