From the Fokker-Planck equation to perturbative QFT's results in de Sitter space

Abstract

A technique to build perturbative series for the spectator field's correlation functions in de Sitter space through the Fokker-Planck equation is proposed. We derive from the first-order differential equation the iterative integral relation for equal- and multi-time correlation functions. With an appropriate integration, the obtained two-point and four-point correlation functions are in agreement with quantum field theory's ones.

To appear in JHEP. Major review: we have reduced the description of the computation routine and the repeated equations in the specific cases. The introduction and the comparison with the literature and the corresponding results from there are expanded. We have also explained the expansion scheme and the initial condition choice