Motivated by the string landscape, the inflationary potential may be high dimensional and complicated. We propose a new way to construct some high-dimensional random potentials, and simulate inflationary dynamics 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 the 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 $10^{-3}–10^{-6}$ of the parameter space volume leads to unique classical trajectories. The rest is ruled out by random bifurcations.

• Received 13 March 2015

DOI:https://doi.org/10.1103/PhysRevD.91.103525