We propose a coarse-graining procedure for describing the superhorizon
dynamics of inflationary tensor modes. Our aim is to formulate a stochastic
description for the statistics of spin-2 modes which seed the background of
gravitational waves from inflation. Using basic principles of quantum
mechanics, we determine a probability density for coarse-grained tensor fields,
which satisfies a stochastic Fokker-Planck equation at superhorizon scales. The
corresponding noise and drift are computable, and depend on the cosmological
system under consideration. Our general formulas are applied to a variety of
cosmological scenarios, also considering cases seldom considered in the context
of stochastic inflation, and which are important for their observational
consequences. We start obtaining the expected expressions for noise and drift
in pure de Sitter and power-law inflation, also including a discussion of
effects of non-attractor phases. We then apply our methods to describe
scenarios with a transition from inflation to standard cosmological eras of
radiation and matter domination. We show how the interference between modes
flowing through the cosmological horizon, and modes spontaneously produced at
superhorizon scales, can affect the stochastic evolution of coarse-grained
tensor quantities. In appropriate limits, we find that the corresponding
spectrum of tensor modes at horizon crossing matches with the results of
quantum field theory calculations, but we also highlight where differences can
arise.Comment: 27 pages, 2 figure
