STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNIVERSE

@article{Starobinsky1986STOCHASTICDS,
  title={STOCHASTIC DE SITTER (INFLATIONARY) STAGE IN THE EARLY UNIVERSE},
  author={Alexei A. Starobinsky},
  journal={Lecture Notes in Physics},
  year={1986},
  volume={246},
  pages={107-126}
}
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… 
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