Stochastic de sitter (inflationary) stage in the early universe

Abstract

The dynamics of a large-scale quasi-homogeneous scalar field producing the de Sitter (inflationary) stage in the early universe is strongly affected by small-scale quantum fluctuations of the same scalar field and, in this way, becomes stochastic. The evolution of the corresponding large-scale space-time metric follows that of the scalar field and is stochastic also. The Fokker-Planck equation for the evolution of the large-scale scalar field is obtained and solved for an arbitrary scalar field potential. The average duration of the de-Sitter stage in the new inflationary scenario is calculated (only partial results on this problem were known earlier). Applications of the developed formalism to the chaotic inflationary scenario and to quantum inflation are considered. In these cases, the main unsolved problem lies in initial pre-inflationary conditions.