Stochastic Dynamics of an Inflationary Model and Initial Distribution of Universes

Abstract

We investigate the stationary solution of the modified Fokker Planck equation which governs the global dynamics of the inflation. Contrary to the original FP equation which is for a: Hubble horizon size region, we found that the normalizable stationary solution can exist for modified Fokker-Planck equation which is for many Hubble horizon size regions. For a chaotic inflationary model with the potential Aq:>2n, we get initial distribution of classical universes using this solution, and discussed the physical meaning of it. Especially for n=2, this distribution obeys power-law and classical universes which, created from the Planck energy region, make the fractal structure. In other cases n=l=2, creation of large classical universes is strongly suppressed.