Multi-Stage and Multi-Field Inflation in Random Inflationary Landscapes

Generic potentials in an inflationary landscape are typically too steep to support a prolonged period of cosmic inflation. Atypical flat regions of the landscape are required to support successful inflation. The occurrence of such regions leads broadly to two possibilities: a single prolonged period of slow-roll inflation (which we call single-stage inflation), or multiple shorter periods of inflation separated by transient departures from slow roll (which we call multi-stage inflation), giving rise to primordial features and other departures from the behavior of the simplest slow-roll model. The former is the possibility most commonly assumed when deriving the primordial density fluctuations for the Big Bang model. In this paper, using Gaussian random potentials as a simple model of the inflationary landscape, we study the relative occurrence of these two possibilities. We find a substantial fraction of multi-stage inflationary trajectories in landscapes with field-space dimensions one, two, and three, and this fraction increases with dimensionality at fixed typical landscape curvature. In constructing the inflationary landscapes and identifying successful inflationary trajectories, we also define several relevant quantities and classify detailed properties of both multi-stage and multi-field inflationary trajectories.