Stochastic approach to gravitational waves from inflation

We propose a coarse-graining procedure for describing the superhorizon dynamics of inflationary tensor modes. Our aim is to formulate stochastic description statistics spin-2 modes which seed background gravitational waves from inflation. Using basic principles quantum mechanics, we determine probability density coarse-grained fields, satisfies Fokker-Planck equation at scales. The corresponding noise and drift are computable, depend on cosmological system under consideration. general formulas applied variety scenarios, also considering cases seldom considered in context inflation, important their observational consequences. start obtaining expected expressions pure de Sitter power-law including discussion effects non-attractor phases. then apply our methods describe scenarios with transition inflation standard eras radiation matter domination. show how interference between flowing through horizon, spontaneously produced scales, can affect evolution quantities. In appropriate limits, find that spectrum horizon crossing matches results field theory calculations, but highlight where differences arise.