Supercurvature Modes from Preheating in an Open Universe
  Preheating following the inflationary phase in models of open inflation is considered. The most significant difference from a preheating scenario in flat space is that supercurvature modes can be populated and amplified in the open universe. In certain models, such modes can dominate the usual resonant particle production, thus altering the ensuing thermal history within an open universe. The accuracy to which the masses and couplings need to be tuned to produce such supercurvature modes, however, makes any large deviation from the flat space cases unlikely. 
David I. Kaiser