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Inflation in the early Universe is a grand phase transition which haveproduced the seeds of all the structures we now observe. We focus on thenon-equilibrium aspect of this phase transition especially the inevitableinfrared (IR) divergence associated to the the quantum and classical fieldsduring the inflation. There is a long history of research for removing this IRdivergence for healthy perturbation calculations. On the other hand, the sameIR divergence is quite relevant and have developed the primordial densityfluctuations in the early Universe. We develop a unified formalism in which theIR divergence is clearly separated from the microscopic quantum field theorybut only appear in the statistical classical structure. We derive the classicalLangevin equation for the order parameter within the quantum field theorythrough the instability of the de Sitter vacuum during the inflation. Thisseparation process is relevant in general to develop macroscopic structures andto derive the basic properties of statistical mechanics in the quantum fieldtheory.

Infrared Divergence Separated for Stochastic Force - Langevin Evolution in the Inflationary Era