On decoherence of cosmological perturbations and stochastic inflation
  By making a suitable generalization of the Starobinsky stochastic inflation,
we propose a classical phase space formulation of stochastic inflation which
may be used for a quantitative study of decoherence of cosmological
perturbations during inflation. The precise knowledge of how much cosmological
perturbations have decohered is essential to the understanding of acoustic
oscillations of cosmological microwave background (CMB) photons. In order to
show how the method works, we provide the relevant equations for a
self-interacting inflaton field. For pedagogical reasons and to provide a link
to the field theoretical case, we consider the quantum stochastic harmonic
oscillator.
